A blowing-up formula for the intersection cohomology of the moduli of rank 2 Higgs bundles over a curve with trivial determinant

TL;DR

This paper establishes a blowing-up formula for the intersection cohomology of rank 2 Higgs bundle moduli spaces over a curve with trivial determinant, enabling computation of their Poincaré polynomial.

Contribution

It introduces a new blowing-up formula for intersection cohomology in the context of Higgs bundle moduli spaces, advancing understanding of their topological invariants.

Findings

Proves a blowing-up formula for intersection cohomology

Derives the Poincaré polynomial of the moduli space

Provides a method under a technical assumption

Abstract

We prove that a blowing-up formula for the intersection cohomology of the moduli space of rank 2 Higgs bundles over a curve with trivial determinant holds. As an application, we derive the Poincar\'{e} polynomial of the intersection cohomology of the moduli space under a technical assumption.