arXiv subjects
Publications and source records attributed to José M. Muñoz Porras.
This paper shows how the Theorem of Residues (TR) and the Gelfand-Fuchs cocycle can be deduced in a simple way from the Weil Reciprocity Law (WRL). Indeed, if one understand WRL as the triviality of certain extension of groups, then TR is the same statement at the level of Lie algebras. Finally, the Gelfand-Fuchs cocycle can also be obtained in this way.
Using the technique of the Fourier-Mukai transform we give an explicit set of generators of the ideal defining an algebraic curve as a subscheme of its Jacobian. Essentially, these ideals are generated by the Fay's trisecant identities.
In this paper we study the Hurwitz scheme in terms of the Sato Grassmannian and the algebro-geometric theory of solitons. We will give a characterization, its equations and a show that there is a group of Virasoro type which uniformizes it.
The main result proved in the paper is the computation of the explicit equations defining the Hurwitz schemes of coverings with punctures as subschemes of the Sato infinite Grassmannian. As an application, we characterize the existence of certain linear series on a smooth curve in terms of soliton equations.