Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective
- 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.
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| Author: | Madeline BrandtORCiD, Martin UlirschORCiDGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-818886 |
| DOI: | https://doi.org/10.1090/btran/113 |
| ISSN: | 2330-0000 |
| ArXiv Id: | http://arxiv.org/abs/1812.08740 |
| Parent Title (English): | Transactions of the American Mathematical Society. Series B |
| Publisher: | American Mathematical Society |
| Place of publication: | Providence, RI |
| Document Type: | Article |
| Language: | English |
| Year of Completion: | 2022 |
| Year of first Publication: | 2022 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2024/02/23 |
| Volume: | 9 |
| Page Number: | 33 |
| First Page: | 586 |
| Last Page: | 618 |
| Institutes: | Informatik und Mathematik / Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - Namensnennung-Nicht kommerziell 3.0 |
