article Madeline Brandt author Martin Ulirsch author 114697 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 eng 1812.0874010.1090/btran/113 M. Brandt, M. Ulirsch, ArXiv:1812.08740 (2018). 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>. 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>. 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> @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} } 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> 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>. 663292026-07-08T06:52:13Z2026-07-08T09:45:46Z