Moduli spaces of anti-invariant vector bundles over a curve

TL;DR

This paper constructs moduli spaces for anti-invariant vector bundles on a curve with an involution, expanding understanding of vector bundle classifications under symmetry conditions.

Contribution

It introduces a method to construct moduli spaces of anti-invariant vector bundles on curves with involution, a novel class of vector bundles.

Findings

Constructed moduli spaces for anti-invariant vector bundles.

Provided new insights into the structure of vector bundles under involution.

Extended the theory of vector bundle moduli to include anti-invariant cases.

Abstract

Let $X$ be a smooth irreducible projective curve with an involution $\sigma$. A vector bundle $E$ over $X$ is called anti-invariant if there exists an isomorphism $\sigma^*E\rightarrow E^*$. In this paper, we give a construction of the moduli spaces of anti-invariant vector bundles over $X$.