# Counting Higgs bundles and type A quiver bundles

## TL;DR

This paper derives explicit formulas for counting semistable twisted Higgs bundles and quiver bundles over algebraic curves, linking these counts to Donaldson-Thomas invariants and providing new combinatorial tools for moduli space analysis.

## Contribution

It introduces closed-form formulas for counting semistable twisted Higgs bundles and quiver bundles, extending previous results to broader classes over finite fields.

## Key findings

- Closed formulas for counting semistable twisted Higgs bundles.
- Explicit expressions for Donaldson-Thomas invariants of Higgs bundle moduli.
- A Harder-Narasimhan-type formula for semistable U(p,q)-bundles.

## Abstract

We prove a closed formula counting semistable twisted (or meromorphic) Higgs bundles of fixed rank and degree over a smooth projective curve of genus g, defined over a finite field, when the degree of the twisting line bundle is at least 2g-2; this includes the case of usual Higgs bundles. We obtain at the same time a closed expression for the Donaldson-Thomas invariants of the moduli spaces of twisted Higgs bundles. We similarly deal with twisted quiver bundles of type A (affine or finite), obtaining in particular a Harder-Narasimhan-type formula counting semistable U(p,q)-bundles over any smooth projective curve over a finite field.