Stable bundles and polyvector fields

TL;DR

This paper constructs an algebra of holomorphic polyvector fields on the moduli space of stable G-bundles over a curve, revealing new algebraic structures and proving a vanishing theorem for degree two in specific cases.

Contribution

It introduces a novel algebra of Schouten-commuting polyvector fields on the moduli space, using invariant Lie algebra forms, and establishes a vanishing theorem for degree two when G=GL(n).

Findings

Constructed an algebra of polyvector fields on the moduli space.

Proved a vanishing theorem for degree two in the case G=GL(n).

Identified generators starting in degree three.

Abstract

We introduce an algebra of Schouten-commuting holomorphic polyvector fields on the moduli space of stable G-bundles over a curve by using invariant forms on the Lie algebra. The generators begin in degree three -- we prove a vanishing theorem for degree two in the case of G=GL(n).