The Vanishing of the Theta Function in the KP Direction: a Geometric Approach
Algebraic Geometry
2007-05-23 v1 Dynamical Systems
Abstract
We give a geometric proof of a formula, due to Segal and Wilson, which describes the order of vanishing of the Riemann theta function in the direction which corresponds to the direction of the tangent space of a Riemann surface at a marked point. While this formula appears in the work of Segal and Wilson as a by-product of some non-trivial constructions from the theory of integrable systems (loop groups, infinite-dimensional Grassmannians, tau functions, Schur polynomials, ...) our proof only uses the classical theory of linear systems on Riemann surfaces.
Keywords
Cite
@article{arxiv.math/0110193,
title = {The Vanishing of the Theta Function in the KP Direction: a Geometric Approach},
author = {Ch. Birkenhake and P. Vanhaecke},
journal= {arXiv preprint arXiv:math/0110193},
year = {2007}
}
Comments
8 pages, latex