The Segre-Verlinde correspondence for the moduli space of stable bundles on a curve

TL;DR

This paper reveals a new correspondence between Verlinde numbers and Segre numbers for the moduli space of semistable vector bundles on a curve, linking two important invariants in algebraic geometry.

Contribution

It establishes a novel Segre-Verlinde correspondence, connecting Verlinde numbers with Segre numbers of universal complexes on the moduli space.

Findings

Verlinde numbers can be interpreted as Segre numbers.

The correspondence provides new insights into the geometry of the moduli space.

Universal complexes encode key geometric information.

Abstract

We show that the classic Verlinde numbers on the moduli space of semistable vector bundles on a smooth projective curve can also be regarded as Segre numbers of natural universal complexes over the moduli space.