[{"abstract":[{"text":"<jats:p>We contribute to the foundations of tropical geometry with a view toward formulating tropical moduli problems, and with the moduli space of curves as our main example. We propose a moduli functor for the moduli space of curves and show that it is representable by a geometric stack over the category of rational polyhedral cones. In this framework, the natural forgetful morphisms between moduli spaces of curves with marked points function as universal curves.</jats:p>\r\n\t  <jats:p>Our approach to tropical geometry permits tropical moduli problems—moduli of curves or otherwise—to be extended to logarithmic schemes. We use this to construct a smooth tropicalization morphism from the moduli space of algebraic curves to the moduli space of tropical curves, and we show that this morphism commutes with all of the tautological morphisms.</jats:p>","lang":"eng"}],"publication":"Forum of Mathematics, Sigma","citation":{"short":"R. Cavalieri, M. Chan, M. Ulirsch, J. Wise, Forum of Mathematics, Sigma 8 (2020).","chicago":"Cavalieri, Renzo, Melody Chan, Martin Ulirsch, and Jonathan Wise. “A MODULI STACK OF TROPICAL CURVES.” <i>Forum of Mathematics, Sigma</i> 8 (2020). <a href=\"https://doi.org/10.1017/fms.2020.16\">https://doi.org/10.1017/fms.2020.16</a>.","apa":"Cavalieri, R., Chan, M., Ulirsch, M., &#38; Wise, J. (2020). A MODULI STACK OF TROPICAL CURVES. <i>Forum of Mathematics, Sigma</i>, <i>8</i>, Article e23. <a href=\"https://doi.org/10.1017/fms.2020.16\">https://doi.org/10.1017/fms.2020.16</a>","ieee":"R. Cavalieri, M. Chan, M. Ulirsch, and J. Wise, “A MODULI STACK OF TROPICAL CURVES,” <i>Forum of Mathematics, Sigma</i>, vol. 8, Art. no. e23, 2020, doi: <a href=\"https://doi.org/10.1017/fms.2020.16\">10.1017/fms.2020.16</a>.","ama":"Cavalieri R, Chan M, Ulirsch M, Wise J. A MODULI STACK OF TROPICAL CURVES. <i>Forum of Mathematics, Sigma</i>. 2020;8. doi:<a href=\"https://doi.org/10.1017/fms.2020.16\">10.1017/fms.2020.16</a>","bibtex":"@article{Cavalieri_Chan_Ulirsch_Wise_2020, title={A MODULI STACK OF TROPICAL CURVES}, volume={8}, DOI={<a href=\"https://doi.org/10.1017/fms.2020.16\">10.1017/fms.2020.16</a>}, number={e23}, journal={Forum of Mathematics, Sigma}, publisher={Cambridge University Press (CUP)}, author={Cavalieri, Renzo and Chan, Melody and Ulirsch, Martin and Wise, Jonathan}, year={2020} }","mla":"Cavalieri, Renzo, et al. “A MODULI STACK OF TROPICAL CURVES.” <i>Forum of Mathematics, Sigma</i>, vol. 8, e23, Cambridge University Press (CUP), 2020, doi:<a href=\"https://doi.org/10.1017/fms.2020.16\">10.1017/fms.2020.16</a>."},"type":"journal_article","date_created":"2026-07-08T07:07:13Z","date_updated":"2026-07-09T07:06:55Z","publication_status":"published","intvolume":"         8","title":"A MODULI STACK OF TROPICAL CURVES","year":"2020","status":"public","publication_identifier":{"issn":["2050-5094"]},"author":[{"last_name":"Cavalieri","first_name":"Renzo","full_name":"Cavalieri, Renzo"},{"first_name":"Melody","last_name":"Chan","full_name":"Chan, Melody"},{"id":"114697","full_name":"Ulirsch, Martin","last_name":"Ulirsch","first_name":"Martin"},{"first_name":"Jonathan","last_name":"Wise","full_name":"Wise, Jonathan"}],"doi":"10.1017/fms.2020.16","user_id":"82981","volume":8,"article_number":"e23","_id":"66336","language":[{"iso":"eng"}],"publisher":"Cambridge University Press (CUP)"}]