Tautological bundles on parabolic moduli spaces: Euler characteristics and Hecke correspondences

TL;DR

This paper computes the Euler characteristic of vector bundles on moduli spaces of stable parabolic bundles using wall-crossing, residue calculus, and Hecke correspondences, extending results related to K-theory indices.

Contribution

It introduces a novel approach combining wall-crossing, residue calculus, and Hecke correspondences to compute Euler characteristics on parabolic moduli spaces.

Findings

Euler characteristics are explicitly calculated for vector bundles on parabolic moduli spaces.

The method extends previous K-theory index results to new geometric contexts.

The approach provides a framework for future computations in moduli space geometry.

Abstract

We calculate the Euler characteristic of associated vector bundles over the moduli spaces of stable parabolic bundles on smooth curves. Our method is based on a wall-crossing technique from Geometric Invariant Theory, certain iterated residue calculus and the tautological Hecke correspondence. Our work was motivated by the results of Teleman and Woodward on the index of K-theory classes on moduli stacks.