Poincare polynomials of moduli spaces of stable bundles over curves

TL;DR

This paper computes the number of stable bundles over finite field curves and derives the virtual Poincare polynomials of their moduli spaces, advancing understanding of their geometric and topological properties.

Contribution

It provides explicit formulas for counting stable bundles and calculating their moduli space invariants, with conjectures extending to Hodge polynomials and motives.

Findings

Explicit count of stable bundles over finite fields.

Calculation of virtual Poincare polynomials of moduli spaces.

Conjectured formulas for Hodge polynomials and motives.

Abstract

Given a curve over a finite field, we compute the number of stable bundles of not necessarily coprime rank and degree over it. We apply this result to compute the virtual Poincare polynomials of the moduli spaces of stable bundles over a curve. A similar formula for the virtual Hodge polynomials and motives is conjectured.