The Vanishing of the Theta Function in the KP Direction: a Geometric Approach

Details The Vanishing of the Theta Function in the KP Direction: a Geometric Approach The Vanishing of the Theta Function in the KP Direction: a Geometric Approach

2001-10-18

arxiv.org/abs/math/0110193v1

Mathematics

Algebraic Geometry

8 pages, latex

Scientific paper

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.

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