A solution of the Schottky-Type problem for curves with automorphisms
  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. 
E. G\'omez, J. M. Mu\~noz, F. J. Plaza, S. Recillas, R. E. Rodr\'iguez