{"author":[{"full_name":"Brandt, Madeline","last_name":"Brandt","first_name":"Madeline"},{"id":"114697","first_name":"Martin","last_name":"Ulirsch","full_name":"Ulirsch, Martin"}],"status":"public","title":"Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective","year":"2018","date_updated":"2026-07-08T09:45:46Z","_id":"66329","language":[{"iso":"eng"}],"user_id":"82981","doi":"10.1090/btran/113","citation":{"apa":"Brandt, M., &#38; Ulirsch, M. (2018). Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective. <i>ArXiv:1812.08740</i>. <a href=\"https://doi.org/10.1090/btran/113\">https://doi.org/10.1090/btran/113</a>","ieee":"M. Brandt and M. Ulirsch, “Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective,” <i>arXiv:1812.08740</i>, 2018, doi: <a href=\"https://doi.org/10.1090/btran/113\">10.1090/btran/113</a>.","chicago":"Brandt, Madeline, and Martin Ulirsch. “Symmetric Powers of Algebraic and Tropical Curves: A Non-Archimedean Perspective.” <i>ArXiv:1812.08740</i>, 2018. <a href=\"https://doi.org/10.1090/btran/113\">https://doi.org/10.1090/btran/113</a>.","short":"M. Brandt, M. Ulirsch, ArXiv:1812.08740 (2018).","mla":"Brandt, Madeline, and Martin Ulirsch. “Symmetric Powers of Algebraic and Tropical Curves: A Non-Archimedean Perspective.” <i>ArXiv:1812.08740</i>, 2018, doi:<a href=\"https://doi.org/10.1090/btran/113\">10.1090/btran/113</a>.","ama":"Brandt M, Ulirsch M. Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective. <i>arXiv:181208740</i>. Published online 2018. doi:<a href=\"https://doi.org/10.1090/btran/113\">10.1090/btran/113</a>","bibtex":"@article{Brandt_Ulirsch_2018, title={Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective}, DOI={<a href=\"https://doi.org/10.1090/btran/113\">10.1090/btran/113</a>}, journal={arXiv:1812.08740}, author={Brandt, Madeline and Ulirsch, Martin}, year={2018} }"},"publication":"arXiv:1812.08740","abstract":[{"lang":"eng","text":"We show that the non-Archimedean skeleton of the $d$-th symmetric power of a smooth projective algebraic curve $X$ is naturally isomorphic to the $d$-th symmetric power of the tropical curve that arises as the non-Archimedean skeleton of $X$. The retraction to the skeleton is precisely the specialization map for divisors. Moreover, we show that the process of tropicalization naturally commutes with the diagonal morphisms and the Abel-Jacobi map and we exhibit a faithful tropicalization for symmetric powers of curves. Finally, we prove a version of the Bieri-Groves Theorem that allows us, under certain tropical genericity assumptions, to deduce a new tropical Riemann-Roch-Theorem for the tropicalization of linear systems."}],"date_created":"2026-07-08T06:52:13Z","external_id":{"arxiv":["1812.08740"]},"type":"journal_article"}