Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective
M. Brandt, M. Ulirsch, Transactions of the American Mathematical Society, Series B 9 (2022) 586–618.
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Journal Article
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| English
Author
Brandt, Madeline;
Ulirsch, MartinLibreCat
Abstract
<p>
We show that the non-Archimedean skeleton of the
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-th symmetric power of a smooth projective algebraic curve
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is naturally isomorphic to the
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-th symmetric power of the tropical curve that arises as the non-Archimedean skeleton of
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. 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.
</p>
Publishing Year
Journal Title
Transactions of the American Mathematical Society, Series B
Volume
9
Issue
20
Page
586-618
ISSN
LibreCat-ID
Cite this
Brandt M, Ulirsch M. Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective. Transactions of the American Mathematical Society, Series B. 2022;9(20):586-618. doi:10.1090/btran/113
Brandt, M., & Ulirsch, M. (2022). Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective. Transactions of the American Mathematical Society, Series B, 9(20), 586–618. https://doi.org/10.1090/btran/113
@article{Brandt_Ulirsch_2022, title={Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective}, volume={9}, DOI={10.1090/btran/113}, number={20}, journal={Transactions of the American Mathematical Society, Series B}, publisher={American Mathematical Society (AMS)}, author={Brandt, Madeline and Ulirsch, Martin}, year={2022}, pages={586–618} }
Brandt, Madeline, and Martin Ulirsch. “Symmetric Powers of Algebraic and Tropical Curves: A Non-Archimedean Perspective.” Transactions of the American Mathematical Society, Series B 9, no. 20 (2022): 586–618. https://doi.org/10.1090/btran/113.
M. Brandt and M. Ulirsch, “Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective,” Transactions of the American Mathematical Society, Series B, vol. 9, no. 20, pp. 586–618, 2022, doi: 10.1090/btran/113.
Brandt, Madeline, and Martin Ulirsch. “Symmetric Powers of Algebraic and Tropical Curves: A Non-Archimedean Perspective.” Transactions of the American Mathematical Society, Series B, vol. 9, no. 20, American Mathematical Society (AMS), 2022, pp. 586–618, doi:10.1090/btran/113.
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