Rationality of Moduli Spaces of Parabolic Bundles

TL;DR

This paper proves the rationality of certain moduli spaces of parabolic bundles over curves, showing that under specific conditions, these spaces are rational or stably rational, advancing understanding of their geometric structure.

Contribution

It establishes the rationality of moduli spaces of parabolic bundles with fixed determinant when a multiplicity is one, and deduces rationality results for vector bundle moduli spaces.

Findings

Moduli space of parabolic bundles is rational if a multiplicity equals one.

Under coprimality of rank and degree, the moduli space is stably rational.

The bound on the level is sufficient to conclude rationality in many cases.

Abstract

The moduli space of parabolic bundles with fixed determinant over a smooth curve of genus greater than one is proved to be rational whenever one of the multiplicities associated to the quasi-parabolic structure is equal to one. It follows that if rank and degree are coprime, the moduli space of vector bundles is stably rational, and the bound obtained on the level is strong enough to conclude rationality in many cases.