TY  - JOUR
A1  - Brandt, Madeline
A1  - Ulirsch, Martin
T1  - Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective
T2  - Transactions of the American Mathematical Society. Series B
N2  - 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.
Y1  - 2022
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/81888
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-818886
SN  - 2330-0000
N1  - Gefördert durch den Open-Access-Publikationsfonds der Goethe-Universität.
VL  - 9
SP  - 586
EP  - 618
PB  - American Mathematical Society
CY  - Providence, RI
ER  -