Intersection numbers on moduli spaces and symmetries of a Verlinde formula

TL;DR

This paper explores the geometry of moduli spaces of stable bundles on Riemann surfaces and extends the Verlinde formula to compute intersection pairings, revealing new symmetries and structural insights.

Contribution

It introduces a generalized Verlinde formula applicable to intersection pairings on moduli spaces, highlighting novel symmetries and geometric properties.

Findings

Derived new intersection number formulas for moduli spaces

Identified symmetries in the Verlinde formula

Enhanced understanding of the topology of stable bundle moduli spaces

Abstract

We investigate the geometry and topology of a standard moduli space of stable bundles on a Riemann surface, and use a generalization of the Verlinde formula to derive results on intersection pairings.