Hostname: page-component-cb9f654ff-plnhv Total loading time: 0.001 Render date: 2025-08-18T17:32:58.020Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  04 December 2007

Christina Birkenhake  and
Pol Vanhaecke
Christina Birkenhake
Affiliation:
Mathematisches Institut, Bismarkstrasse 1 1/2, D-91054 Erlangen. Germany. e-mail: birken@mi.uni-erlangen.de
Pol Vanhaecke
Affiliation:
Université de Poitiers, Département de Poitiers, Téléport 2, Boulevard Marie et Pierre Curie, BP 30179, F-86962 Futuroscope Chasseneuil Cedex, France. e-mail: Pol.Vanhaecke@mathlabo.univ-poitiers.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 nontrivial constructions from the theory of integrable systems (loop groups, infinite-dimensional Grassmannians, tau functions, Schur polynomials, etc.) our proof only uses the classical theory of linear systems on Riemann surfaces.

Keywords

gap sequencesJacobianstheta functions

Information

Type
Research Article
Information
Compositio Mathematica , Volume 135 , Issue 3 , February 2003 , pp. 323 - 330
Copyright
© 2003 Kluwer Academic Publishers