2026-09-05T19:17:04Zhttps://gredos.usal.es/oai/request

oai:gredos.usal.es:10366/1593022026-01-20T17:56:20Zcom_10366_4540com_10366_4512com_10366_3823col_10366_4541

Gómez González, Esteban Muñoz Porras, José María Plaza Martín, Francisco José Rodríguez, Rubí Elena 2024-08-26T08:37:41Z 2024-08-26T08:37:41Z 2010 0002-9947 http://hdl.handle.net/10366/159302 10.1090/S0002-9947-2010-05029-9 [EN] We obtain a characterization of theta functions of Jacobian vari eties of curves with automorphisms among theta functions of principally po larized abelian varieties (p.p.a.v.). We first give a characterization in terms of finite dimensional orbits for a suitable action in the Sato Grassmannian. Secondly, the introduction of formal Baker-Akhiezer functions and formal τ functions attached to a p.p.a.v. (for the multipuncture case) allows us to char acterize, in terms of bilinear identities, those Baker-Akhiezer functions that are Baker-Akhiezer functions of Jacobians of curves with automorphisms. Further, in the case of automorphisms with fixed points, we rewrite the previous result as a hierarchy of partial differential equations for the τ-function of a p.p.a.v. Finally, since Baker-Akhiezer and τ functions are written in terms of theta functions, these results give rise to characterizations of p.p.a.v. in terms of their theta functions. eng AMS. American Mathematical Society Characterizations of Jacobians of curves with automorphisms info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://doi.org/10.1090/S0002-9947-2010-05029-9 info:eu-repo/semantics/openAccess Transactions of the American Mathematical Society 362 10 5373 5373