Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective Brandt, Madeline Ulirsch, Martin 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. 2018 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://ris.uni-paderborn.de/record/66329 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1090/btran/113 info:eu-repo/semantics/altIdentifier/arxiv/1812.08740 info:eu-repo/semantics/closedAccess