Hecke transformation for orthogonal bundles and stability of Picard bundles

TL;DR

This paper introduces Hecke transformations for orthogonal bundles over Riemann surfaces and proves the stability of the associated Picard bundle on the moduli space using these transformations.

Contribution

It defines Hecke transformations for orthogonal bundles and demonstrates the stability of the Picard bundle on the moduli space, a novel application in this context.

Findings

Hecke transformations for orthogonal bundles are successfully defined.

The projectivized Picard bundle on the moduli space is proven to be stable.

The approach uses cycles on the moduli space induced by Hecke transformations.

Abstract

We define Hecke transformation for orthogonal bundles over a compact Riemann surface. Using the cycles on a moduli space of orthogonal bundles given by Hecke transformations, we prove that the projectivized Picard bundle on the moduli space is stable.