Moduli spaces of stable bundles on ruled 3-folds and Brill-Noether problems

TL;DR

This paper develops a new approach to study moduli spaces of stable rank 2 vector bundles on higher-dimensional algebraic varieties, specifically ruled 3-folds, and demonstrates the non-emptiness of certain Brill-Noether loci.

Contribution

It introduces a novel method for analyzing walls and chambers in moduli spaces, extending the theory to higher dimensions and applying it to specific geometric problems.

Findings

Description of components of moduli spaces of rank 2 stable bundles on ruled 3-folds

Proof of non-emptiness of some Brill-Noether loci

Development of a new tool for studying stability conditions in higher dimensions

Abstract

In this paper, we redefine the theory of walls and chambers due to Qin developing a new tool to study moduli spaces of stable rank 2 vector bundles on algebraic varieties of higher dimension. We apply it to describe components of some moduli spaces of rank 2 stable bundles on ruled 3-folds as well as to prove that some Brill-Noether loci are non-empty.