Symmetric theta divisors of Klein surfaces

Teleman, Andrei ; Okonek, Christian

HAL, hal-00881499 / Harvested from HAL

Résumé

This is a slightly expanded version of the talk given by Ch.O. at the conference "Instantons in complex geometry", at the Steklov Institute in Moscow. The purpose of this talk was to explain the algebraic results of our paper "Abelian Yang-Mills theory on Real tori and Theta divisors of Klein surfaces". In this paper we compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the corresponding Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein surface these determinant index bundles have a natural holomorphic description as theta line bundles. In particular we compute the first Stiefel-Whitney classes of the corresponding fixed point bundles on the real part of the Picard torus. The computation of these classes is important, because they control to a large extent the orientability of certain moduli spaces in Real gauge theory and Real algebraic geometry.

Détail

Publié le : 2012-08-05
Classification:  Klein surfaces Symmetric theta divisors,  Appell-Humbert data,  Yang-Mills connections,  Real vector bundles,  MSC 14H55 14H60 14H40,  [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG],  [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]