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

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

2005-06-10

arxiv.org/abs/math/0506194v1

Mathematics

Algebraic Geometry

Scientific paper

In this paper, an explicit hierarchy of differential equations for the $\tau$-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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