[{"date_updated":"2026-07-08T06:49:19Z","year":"2019","title":"Tropical double ramification loci","status":"public","author":[{"id":"114697","full_name":"Ulirsch, Martin","last_name":"Ulirsch","first_name":"Martin"},{"full_name":"Zakharov, Dmitry","last_name":"Zakharov","first_name":"Dmitry"}],"user_id":"82981","language":[{"iso":"eng"}],"_id":"66322","abstract":[{"text":"Motivated by the realizability problem for principal tropical divisors with a fixed ramification profile, we explore the tropical geometry of the double ramification locus in $\\mathcal{M}_{g,n}$.There are two ways to define a tropical analogue of the double ramification locus: one as a locus of principal divisors, the other as a locus of finite effective ramified covers of a tree. We show that both loci admit a structure of a generalized cone complex in $M_{g,n}^{trop}$, with the latter contained in the former. We prove that the locus of principal divisors has cones of codimension zero in $M_{g,n}^{trop}$, while the locus of ramified covers has the expected codimension $g$. This solves the deformation-theoretic part of the realizability problem for principal divisors, reducing it to the so-called Hurwitz existence problem for covers of a fixed ramification type.","lang":"eng"}],"publication":"arXiv:1910.01499","citation":{"mla":"Ulirsch, Martin, and Dmitry Zakharov. “Tropical Double Ramification Loci.” <i>ArXiv:1910.01499</i>, 2019.","bibtex":"@article{Ulirsch_Zakharov_2019, title={Tropical double ramification loci}, journal={arXiv:1910.01499}, author={Ulirsch, Martin and Zakharov, Dmitry}, year={2019} }","ama":"Ulirsch M, Zakharov D. Tropical double ramification loci. <i>arXiv:191001499</i>. Published online 2019.","ieee":"M. Ulirsch and D. Zakharov, “Tropical double ramification loci,” <i>arXiv:1910.01499</i>. 2019.","apa":"Ulirsch, M., &#38; Zakharov, D. (2019). Tropical double ramification loci. In <i>arXiv:1910.01499</i>.","short":"M. Ulirsch, D. Zakharov, ArXiv:1910.01499 (2019).","chicago":"Ulirsch, Martin, and Dmitry Zakharov. “Tropical Double Ramification Loci.” <i>ArXiv:1910.01499</i>, 2019."},"type":"preprint","external_id":{"arxiv":["1910.01499"]},"date_created":"2026-07-08T06:49:12Z"},{"intvolume":"       291","date_updated":"2026-07-09T07:34:26Z","publication_status":"published","publication_identifier":{"issn":["0025-5874","1432-1823"]},"author":[{"full_name":"Foster, Tyler","first_name":"Tyler","last_name":"Foster"},{"first_name":"Dhruv","last_name":"Ranganathan","full_name":"Ranganathan, Dhruv"},{"full_name":"Talpo, Mattia","first_name":"Mattia","last_name":"Talpo"},{"id":"114697","full_name":"Ulirsch, Martin","first_name":"Martin","last_name":"Ulirsch"}],"status":"public","year":"2018","title":"Logarithmic Picard groups, chip firing, and the combinatorial rank","volume":291,"doi":"10.1007/s00209-018-2085-2","user_id":"82981","publisher":"Springer Science and Business Media LLC","_id":"66338","language":[{"iso":"eng"}],"page":"313-327","citation":{"mla":"Foster, Tyler, et al. “Logarithmic Picard Groups, Chip Firing, and the Combinatorial Rank.” <i>Mathematische Zeitschrift</i>, vol. 291, no. 1–2, Springer Science and Business Media LLC, 2018, pp. 313–27, doi:<a href=\"https://doi.org/10.1007/s00209-018-2085-2\">10.1007/s00209-018-2085-2</a>.","ama":"Foster T, Ranganathan D, Talpo M, Ulirsch M. Logarithmic Picard groups, chip firing, and the combinatorial rank. <i>Mathematische Zeitschrift</i>. 2018;291(1-2):313-327. doi:<a href=\"https://doi.org/10.1007/s00209-018-2085-2\">10.1007/s00209-018-2085-2</a>","bibtex":"@article{Foster_Ranganathan_Talpo_Ulirsch_2018, title={Logarithmic Picard groups, chip firing, and the combinatorial rank}, volume={291}, DOI={<a href=\"https://doi.org/10.1007/s00209-018-2085-2\">10.1007/s00209-018-2085-2</a>}, number={1–2}, journal={Mathematische Zeitschrift}, publisher={Springer Science and Business Media LLC}, author={Foster, Tyler and Ranganathan, Dhruv and Talpo, Mattia and Ulirsch, Martin}, year={2018}, pages={313–327} }","apa":"Foster, T., Ranganathan, D., Talpo, M., &#38; Ulirsch, M. (2018). Logarithmic Picard groups, chip firing, and the combinatorial rank. <i>Mathematische Zeitschrift</i>, <i>291</i>(1–2), 313–327. <a href=\"https://doi.org/10.1007/s00209-018-2085-2\">https://doi.org/10.1007/s00209-018-2085-2</a>","ieee":"T. Foster, D. Ranganathan, M. Talpo, and M. Ulirsch, “Logarithmic Picard groups, chip firing, and the combinatorial rank,” <i>Mathematische Zeitschrift</i>, vol. 291, no. 1–2, pp. 313–327, 2018, doi: <a href=\"https://doi.org/10.1007/s00209-018-2085-2\">10.1007/s00209-018-2085-2</a>.","short":"T. Foster, D. Ranganathan, M. Talpo, M. Ulirsch, Mathematische Zeitschrift 291 (2018) 313–327.","chicago":"Foster, Tyler, Dhruv Ranganathan, Mattia Talpo, and Martin Ulirsch. “Logarithmic Picard Groups, Chip Firing, and the Combinatorial Rank.” <i>Mathematische Zeitschrift</i> 291, no. 1–2 (2018): 313–27. <a href=\"https://doi.org/10.1007/s00209-018-2085-2\">https://doi.org/10.1007/s00209-018-2085-2</a>."},"publication":"Mathematische Zeitschrift","issue":"1-2","type":"journal_article","date_created":"2026-07-08T07:08:39Z"},{"type":"journal_article","date_created":"2026-07-08T07:06:48Z","publication":"Journal of Pure and Applied Algebra","issue":"5","citation":{"chicago":"Huszar, Alana, Steffen Marcus, and Martin Ulirsch. “Clutching and Gluing in Tropical and Logarithmic Geometry.” <i>Journal of Pure and Applied Algebra</i> 223, no. 5 (2018): 2036–61. <a href=\"https://doi.org/10.1016/j.jpaa.2018.08.014\">https://doi.org/10.1016/j.jpaa.2018.08.014</a>.","short":"A. Huszar, S. Marcus, M. Ulirsch, Journal of Pure and Applied Algebra 223 (2018) 2036–2061.","ieee":"A. Huszar, S. Marcus, and M. Ulirsch, “Clutching and gluing in tropical and logarithmic geometry,” <i>Journal of Pure and Applied Algebra</i>, vol. 223, no. 5, pp. 2036–2061, 2018, doi: <a href=\"https://doi.org/10.1016/j.jpaa.2018.08.014\">10.1016/j.jpaa.2018.08.014</a>.","apa":"Huszar, A., Marcus, S., &#38; Ulirsch, M. (2018). Clutching and gluing in tropical and logarithmic geometry. <i>Journal of Pure and Applied Algebra</i>, <i>223</i>(5), 2036–2061. <a href=\"https://doi.org/10.1016/j.jpaa.2018.08.014\">https://doi.org/10.1016/j.jpaa.2018.08.014</a>","bibtex":"@article{Huszar_Marcus_Ulirsch_2018, title={Clutching and gluing in tropical and logarithmic geometry}, volume={223}, DOI={<a href=\"https://doi.org/10.1016/j.jpaa.2018.08.014\">10.1016/j.jpaa.2018.08.014</a>}, number={5}, journal={Journal of Pure and Applied Algebra}, publisher={Elsevier BV}, author={Huszar, Alana and Marcus, Steffen and Ulirsch, Martin}, year={2018}, pages={2036–2061} }","ama":"Huszar A, Marcus S, Ulirsch M. Clutching and gluing in tropical and logarithmic geometry. <i>Journal of Pure and Applied Algebra</i>. 2018;223(5):2036-2061. doi:<a href=\"https://doi.org/10.1016/j.jpaa.2018.08.014\">10.1016/j.jpaa.2018.08.014</a>","mla":"Huszar, Alana, et al. “Clutching and Gluing in Tropical and Logarithmic Geometry.” <i>Journal of Pure and Applied Algebra</i>, vol. 223, no. 5, Elsevier BV, 2018, pp. 2036–61, doi:<a href=\"https://doi.org/10.1016/j.jpaa.2018.08.014\">10.1016/j.jpaa.2018.08.014</a>."},"user_id":"82981","doi":"10.1016/j.jpaa.2018.08.014","volume":223,"page":"2036-2061","_id":"66334","language":[{"iso":"eng"}],"publisher":"Elsevier BV","publication_status":"published","date_updated":"2026-07-09T06:50:37Z","intvolume":"       223","year":"2018","title":"Clutching and gluing in tropical and logarithmic geometry","status":"public","author":[{"full_name":"Huszar, Alana","last_name":"Huszar","first_name":"Alana"},{"last_name":"Marcus","first_name":"Steffen","full_name":"Marcus, Steffen"},{"first_name":"Martin","last_name":"Ulirsch","full_name":"Ulirsch, Martin","id":"114697"}],"publication_identifier":{"issn":["0022-4049"]}},{"intvolume":"       114","publication_status":"published","date_updated":"2026-07-09T07:31:48Z","author":[{"id":"114697","last_name":"Ulirsch","first_name":"Martin","full_name":"Ulirsch, Martin"}],"publication_identifier":{"issn":["0024-6115","1460-244X"]},"title":"Functorial tropicalization of logarithmic schemes: the case of constant coefficients","year":"2017","status":"public","volume":114,"user_id":"82981","doi":"10.1112/plms.12031","_id":"66354","language":[{"iso":"eng"}],"publisher":"Wiley","page":"1081-1113","citation":{"mla":"Ulirsch, Martin. “Functorial Tropicalization of Logarithmic Schemes: The Case of Constant Coefficients.” <i>Proceedings of the London Mathematical Society</i>, vol. 114, no. 6, Wiley, 2017, pp. 1081–113, doi:<a href=\"https://doi.org/10.1112/plms.12031\">10.1112/plms.12031</a>.","ama":"Ulirsch M. Functorial tropicalization of logarithmic schemes: the case of constant coefficients. <i>Proceedings of the London Mathematical Society</i>. 2017;114(6):1081-1113. doi:<a href=\"https://doi.org/10.1112/plms.12031\">10.1112/plms.12031</a>","bibtex":"@article{Ulirsch_2017, title={Functorial tropicalization of logarithmic schemes: the case of constant coefficients}, volume={114}, DOI={<a href=\"https://doi.org/10.1112/plms.12031\">10.1112/plms.12031</a>}, number={6}, journal={Proceedings of the London Mathematical Society}, publisher={Wiley}, author={Ulirsch, Martin}, year={2017}, pages={1081–1113} }","apa":"Ulirsch, M. (2017). Functorial tropicalization of logarithmic schemes: the case of constant coefficients. <i>Proceedings of the London Mathematical Society</i>, <i>114</i>(6), 1081–1113. <a href=\"https://doi.org/10.1112/plms.12031\">https://doi.org/10.1112/plms.12031</a>","ieee":"M. Ulirsch, “Functorial tropicalization of logarithmic schemes: the case of constant coefficients,” <i>Proceedings of the London Mathematical Society</i>, vol. 114, no. 6, pp. 1081–1113, 2017, doi: <a href=\"https://doi.org/10.1112/plms.12031\">10.1112/plms.12031</a>.","short":"M. Ulirsch, Proceedings of the London Mathematical Society 114 (2017) 1081–1113.","chicago":"Ulirsch, Martin. “Functorial Tropicalization of Logarithmic Schemes: The Case of Constant Coefficients.” <i>Proceedings of the London Mathematical Society</i> 114, no. 6 (2017): 1081–1113. <a href=\"https://doi.org/10.1112/plms.12031\">https://doi.org/10.1112/plms.12031</a>."},"issue":"6","publication":"Proceedings of the London Mathematical Society","type":"journal_article","date_created":"2026-07-08T07:24:50Z"},{"type":"book_chapter","place":"New York, NY","date_created":"2026-07-08T07:08:13Z","citation":{"mla":"Lin, Bo, and Martin Ulirsch. “Towards a Tropical Hodge Bundle.” <i>Fields Institute Communications</i>, Springer New York, 2017, doi:<a href=\"https://doi.org/10.1007/978-1-4939-7486-3_16\">10.1007/978-1-4939-7486-3_16</a>.","ama":"Lin B, Ulirsch M. Towards a tropical Hodge bundle. In: <i>Fields Institute Communications</i>. Springer New York; 2017. doi:<a href=\"https://doi.org/10.1007/978-1-4939-7486-3_16\">10.1007/978-1-4939-7486-3_16</a>","bibtex":"@inbook{Lin_Ulirsch_2017, place={New York, NY}, title={Towards a tropical Hodge bundle}, DOI={<a href=\"https://doi.org/10.1007/978-1-4939-7486-3_16\">10.1007/978-1-4939-7486-3_16</a>}, booktitle={Fields Institute Communications}, publisher={Springer New York}, author={Lin, Bo and Ulirsch, Martin}, year={2017} }","apa":"Lin, B., &#38; Ulirsch, M. (2017). Towards a tropical Hodge bundle. In <i>Fields Institute Communications</i>. Springer New York. <a href=\"https://doi.org/10.1007/978-1-4939-7486-3_16\">https://doi.org/10.1007/978-1-4939-7486-3_16</a>","ieee":"B. Lin and M. Ulirsch, “Towards a tropical Hodge bundle,” in <i>Fields Institute Communications</i>, New York, NY: Springer New York, 2017.","short":"B. Lin, M. Ulirsch, in: Fields Institute Communications, Springer New York, New York, NY, 2017.","chicago":"Lin, Bo, and Martin Ulirsch. “Towards a Tropical Hodge Bundle.” In <i>Fields Institute Communications</i>. New York, NY: Springer New York, 2017. <a href=\"https://doi.org/10.1007/978-1-4939-7486-3_16\">https://doi.org/10.1007/978-1-4939-7486-3_16</a>."},"publication":"Fields Institute Communications","doi":"10.1007/978-1-4939-7486-3_16","user_id":"82981","_id":"66337","language":[{"iso":"eng"}],"publisher":"Springer New York","date_updated":"2026-07-09T07:03:43Z","publication_status":"published","publication_identifier":{"issn":["1069-5265","2194-1564"],"isbn":["9781493974856","9781493974863"]},"author":[{"first_name":"Bo","last_name":"Lin","full_name":"Lin, Bo"},{"id":"114697","full_name":"Ulirsch, Martin","last_name":"Ulirsch","first_name":"Martin"}],"title":"Towards a tropical Hodge bundle","status":"public","year":"2017"},{"_id":"66349","language":[{"iso":"eng"}],"publisher":"Springer International Publishing","doi":"10.1007/978-3-319-30945-3_9","user_id":"82981","publication_identifier":{"issn":["2365-9564","2365-9572"],"isbn":["9783319309446","9783319309453"]},"author":[{"last_name":"Abramovich","first_name":"Dan","full_name":"Abramovich, Dan"},{"full_name":"Chen, Qile","first_name":"Qile","last_name":"Chen"},{"first_name":"Steffen","last_name":"Marcus","full_name":"Marcus, Steffen"},{"full_name":"Ulirsch, Martin","last_name":"Ulirsch","first_name":"Martin","id":"114697"},{"last_name":"Wise","first_name":"Jonathan","full_name":"Wise, Jonathan"}],"title":"Skeletons and fans of logarithmic structures","status":"public","year":"2016","date_updated":"2026-07-09T06:52:38Z","publication_status":"published","place":"Cham","date_created":"2026-07-08T07:22:18Z","type":"book_chapter","citation":{"mla":"Abramovich, Dan, et al. “Skeletons and Fans of Logarithmic Structures.” <i>Simons Symposia</i>, Springer International Publishing, 2016, doi:<a href=\"https://doi.org/10.1007/978-3-319-30945-3_9\">10.1007/978-3-319-30945-3_9</a>.","ama":"Abramovich D, Chen Q, Marcus S, Ulirsch M, Wise J. Skeletons and fans of logarithmic structures. In: <i>Simons Symposia</i>. Springer International Publishing; 2016. doi:<a href=\"https://doi.org/10.1007/978-3-319-30945-3_9\">10.1007/978-3-319-30945-3_9</a>","bibtex":"@inbook{Abramovich_Chen_Marcus_Ulirsch_Wise_2016, place={Cham}, title={Skeletons and fans of logarithmic structures}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-30945-3_9\">10.1007/978-3-319-30945-3_9</a>}, booktitle={Simons Symposia}, publisher={Springer International Publishing}, author={Abramovich, Dan and Chen, Qile and Marcus, Steffen and Ulirsch, Martin and Wise, Jonathan}, year={2016} }","apa":"Abramovich, D., Chen, Q., Marcus, S., Ulirsch, M., &#38; Wise, J. (2016). Skeletons and fans of logarithmic structures. In <i>Simons Symposia</i>. Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-319-30945-3_9\">https://doi.org/10.1007/978-3-319-30945-3_9</a>","ieee":"D. Abramovich, Q. Chen, S. Marcus, M. Ulirsch, and J. Wise, “Skeletons and fans of logarithmic structures,” in <i>Simons Symposia</i>, Cham: Springer International Publishing, 2016.","chicago":"Abramovich, Dan, Qile Chen, Steffen Marcus, Martin Ulirsch, and Jonathan Wise. “Skeletons and Fans of Logarithmic Structures.” In <i>Simons Symposia</i>. Cham: Springer International Publishing, 2016. <a href=\"https://doi.org/10.1007/978-3-319-30945-3_9\">https://doi.org/10.1007/978-3-319-30945-3_9</a>.","short":"D. Abramovich, Q. Chen, S. Marcus, M. Ulirsch, J. Wise, in: Simons Symposia, Springer International Publishing, Cham, 2016."},"publication":"Simons Symposia"},{"year":"2015","title":"Faithful Realizability of Tropical Curves","status":"public","author":[{"first_name":"Man-Wai","last_name":"Cheung","full_name":"Cheung, Man-Wai"},{"full_name":"Fantini, Lorenzo","first_name":"Lorenzo","last_name":"Fantini"},{"first_name":"Jennifer","last_name":"Park","full_name":"Park, Jennifer"},{"id":"114697","first_name":"Martin","last_name":"Ulirsch","full_name":"Ulirsch, Martin"}],"publication_identifier":{"issn":["1073-7928","1687-0247"]},"date_updated":"2026-07-08T08:39:05Z","publication_status":"published","intvolume":"      2016","page":"4706-4727","publisher":"Oxford University Press (OUP)","_id":"66362","language":[{"iso":"eng"}],"doi":"10.1093/imrn/rnv269","user_id":"82981","volume":2016,"publication":"International Mathematics Research Notices","issue":"15","citation":{"ieee":"M.-W. Cheung, L. Fantini, J. Park, and M. Ulirsch, “Faithful Realizability of Tropical Curves,” <i>International Mathematics Research Notices</i>, vol. 2016, no. 15, pp. 4706–4727, 2015, doi: <a href=\"https://doi.org/10.1093/imrn/rnv269\">10.1093/imrn/rnv269</a>.","apa":"Cheung, M.-W., Fantini, L., Park, J., &#38; Ulirsch, M. (2015). Faithful Realizability of Tropical Curves. <i>International Mathematics Research Notices</i>, <i>2016</i>(15), 4706–4727. <a href=\"https://doi.org/10.1093/imrn/rnv269\">https://doi.org/10.1093/imrn/rnv269</a>","chicago":"Cheung, Man-Wai, Lorenzo Fantini, Jennifer Park, and Martin Ulirsch. “Faithful Realizability of Tropical Curves.” <i>International Mathematics Research Notices</i> 2016, no. 15 (2015): 4706–27. <a href=\"https://doi.org/10.1093/imrn/rnv269\">https://doi.org/10.1093/imrn/rnv269</a>.","short":"M.-W. Cheung, L. Fantini, J. Park, M. Ulirsch, International Mathematics Research Notices 2016 (2015) 4706–4727.","mla":"Cheung, Man-Wai, et al. “Faithful Realizability of Tropical Curves.” <i>International Mathematics Research Notices</i>, vol. 2016, no. 15, Oxford University Press (OUP), 2015, pp. 4706–27, doi:<a href=\"https://doi.org/10.1093/imrn/rnv269\">10.1093/imrn/rnv269</a>.","bibtex":"@article{Cheung_Fantini_Park_Ulirsch_2015, title={Faithful Realizability of Tropical Curves}, volume={2016}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnv269\">10.1093/imrn/rnv269</a>}, number={15}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Cheung, Man-Wai and Fantini, Lorenzo and Park, Jennifer and Ulirsch, Martin}, year={2015}, pages={4706–4727} }","ama":"Cheung M-W, Fantini L, Park J, Ulirsch M. Faithful Realizability of Tropical Curves. <i>International Mathematics Research Notices</i>. 2015;2016(15):4706-4727. doi:<a href=\"https://doi.org/10.1093/imrn/rnv269\">10.1093/imrn/rnv269</a>"},"date_created":"2026-07-08T08:38:51Z","type":"journal_article"},{"type":"journal_article","date_created":"2026-07-08T07:25:16Z","citation":{"ama":"Ulirsch M. Tropical compactification in log-regular varieties. <i>Mathematische Zeitschrift</i>. 2015;280(1-2):195-210. doi:<a href=\"https://doi.org/10.1007/s00209-015-1418-7\">10.1007/s00209-015-1418-7</a>","bibtex":"@article{Ulirsch_2015, title={Tropical compactification in log-regular varieties}, volume={280}, DOI={<a href=\"https://doi.org/10.1007/s00209-015-1418-7\">10.1007/s00209-015-1418-7</a>}, number={1–2}, journal={Mathematische Zeitschrift}, publisher={Springer Science and Business Media LLC}, author={Ulirsch, Martin}, year={2015}, pages={195–210} }","mla":"Ulirsch, Martin. “Tropical Compactification in Log-Regular Varieties.” <i>Mathematische Zeitschrift</i>, vol. 280, no. 1–2, Springer Science and Business Media LLC, 2015, pp. 195–210, doi:<a href=\"https://doi.org/10.1007/s00209-015-1418-7\">10.1007/s00209-015-1418-7</a>.","chicago":"Ulirsch, Martin. “Tropical Compactification in Log-Regular Varieties.” <i>Mathematische Zeitschrift</i> 280, no. 1–2 (2015): 195–210. <a href=\"https://doi.org/10.1007/s00209-015-1418-7\">https://doi.org/10.1007/s00209-015-1418-7</a>.","short":"M. Ulirsch, Mathematische Zeitschrift 280 (2015) 195–210.","apa":"Ulirsch, M. (2015). Tropical compactification in log-regular varieties. <i>Mathematische Zeitschrift</i>, <i>280</i>(1–2), 195–210. <a href=\"https://doi.org/10.1007/s00209-015-1418-7\">https://doi.org/10.1007/s00209-015-1418-7</a>","ieee":"M. Ulirsch, “Tropical compactification in log-regular varieties,” <i>Mathematische Zeitschrift</i>, vol. 280, no. 1–2, pp. 195–210, 2015, doi: <a href=\"https://doi.org/10.1007/s00209-015-1418-7\">10.1007/s00209-015-1418-7</a>."},"issue":"1-2","publication":"Mathematische Zeitschrift","volume":280,"user_id":"82981","doi":"10.1007/s00209-015-1418-7","_id":"66355","language":[{"iso":"eng"}],"publisher":"Springer Science and Business Media LLC","page":"195-210","intvolume":"       280","publication_status":"published","date_updated":"2026-07-09T07:00:13Z","publication_identifier":{"issn":["0025-5874","1432-1823"]},"author":[{"id":"114697","first_name":"Martin","last_name":"Ulirsch","full_name":"Ulirsch, Martin"}],"status":"public","title":"Tropical compactification in log-regular varieties","year":"2015"},{"type":"journal_article","date_created":"2026-07-08T07:24:26Z","citation":{"ieee":"M. Ulirsch, “Tropical geometry of moduli spaces of weighted stable curves,” <i>Journal of the London Mathematical Society</i>, vol. 92, no. 2, pp. 427–450, 2015, doi: <a href=\"https://doi.org/10.1112/jlms/jdv032\">10.1112/jlms/jdv032</a>.","apa":"Ulirsch, M. (2015). Tropical geometry of moduli spaces of weighted stable curves. <i>Journal of the London Mathematical Society</i>, <i>92</i>(2), 427–450. <a href=\"https://doi.org/10.1112/jlms/jdv032\">https://doi.org/10.1112/jlms/jdv032</a>","short":"M. Ulirsch, Journal of the London Mathematical Society 92 (2015) 427–450.","chicago":"Ulirsch, Martin. “Tropical Geometry of Moduli Spaces of Weighted Stable Curves.” <i>Journal of the London Mathematical Society</i> 92, no. 2 (2015): 427–50. <a href=\"https://doi.org/10.1112/jlms/jdv032\">https://doi.org/10.1112/jlms/jdv032</a>.","mla":"Ulirsch, Martin. “Tropical Geometry of Moduli Spaces of Weighted Stable Curves.” <i>Journal of the London Mathematical Society</i>, vol. 92, no. 2, Wiley, 2015, pp. 427–50, doi:<a href=\"https://doi.org/10.1112/jlms/jdv032\">10.1112/jlms/jdv032</a>.","bibtex":"@article{Ulirsch_2015, title={Tropical geometry of moduli spaces of weighted stable curves}, volume={92}, DOI={<a href=\"https://doi.org/10.1112/jlms/jdv032\">10.1112/jlms/jdv032</a>}, number={2}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Ulirsch, Martin}, year={2015}, pages={427–450} }","ama":"Ulirsch M. Tropical geometry of moduli spaces of weighted stable curves. <i>Journal of the London Mathematical Society</i>. 2015;92(2):427-450. doi:<a href=\"https://doi.org/10.1112/jlms/jdv032\">10.1112/jlms/jdv032</a>"},"publication":"Journal of the London Mathematical Society","issue":"2","volume":92,"doi":"10.1112/jlms/jdv032","user_id":"82981","_id":"66352","language":[{"iso":"eng"}],"publisher":"Wiley","page":"427-450","intvolume":"        92","date_updated":"2026-07-09T07:01:53Z","publication_status":"published","publication_identifier":{"issn":["0024-6107","1469-7750"]},"author":[{"full_name":"Ulirsch, Martin","first_name":"Martin","last_name":"Ulirsch","id":"114697"}],"status":"public","title":"Tropical geometry of moduli spaces of weighted stable curves","year":"2015"}]