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A solution of the Schottky-Type problem for curves with automorphisms

E. Gómez·J. M. Muñoz·F. J. Plaza·S. Recillas·R. E. Rodríguez
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Abstract

In this paper, an explicit hierarchy of differential equations for the $τ$-functions defining the moduli space of curves with automorphisms as a subscheme of the Sato Grassmannian is obtained. The Schottky problem for Riemann surfaces with automorphisms consists of characterizing those p.p.a.v. that are Jacobian varieties of a curve with a non-trivial automorphism. A characterization in terms of hierarchies of p.d.e. for theta functions is also given.

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E. Gómez, J. M. Muñoz, F. J. Plaza, S. Recillas, R. E. Rodríguez. 2005-06-10. A solution of the Schottky-Type problem for curves with automorphisms. https://arxiv.org/abs/math/0506194

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