Coverings with prescribed ramification and Virasoro groups

Abstract

In this article we study coverings with prescribed ramification from the point of view of the Sato Grassmannian and of the algebro-geometric theory of solitons. We show that the moduli space of such coverings, which is a Hurwitz scheme, is a subscheme of the Grassmannian. We give its equations and show that there is a Virasoro group that uniformizes it. We also characterize when a curve is a covering in terms of bilinear identities.