Intersection Poincare polynomial for Nagaraj-Seshadri moduli space

TL;DR

This paper calculates Betti numbers and intersection Betti numbers for the moduli space of rank 2 semi-stable torsion-free sheaves over a reducible nodal curve, providing new insights into its topological structure.

Contribution

It introduces explicit computations of Betti and intersection Betti numbers for a specific moduli space on reducible nodal curves, extending previous topological analyses.

Findings

Betti numbers of the moduli space components are explicitly computed.

Intersection Betti numbers of the moduli space are determined.

Results enhance understanding of the topology of moduli spaces on singular curves.

Abstract

We compute Betti numbers of both the components of the moduli space of rank 2 semi-stable torsion-free sheaves with fixed determinant over a reducible nodal curve with two smooth components intersecting at a node. We also compute the intersection Betti numbers of the moduli space.