Disconnected moduli spaces of stable bundles on surfaces

TL;DR

This paper constructs new examples of vector bundles on surfaces and reveals that the moduli spaces of rank 2 stable bundles can have arbitrarily many connected components, challenging previous assumptions.

Contribution

It introduces hypersurface-based methods to produce vector bundles and demonstrates the existence of moduli spaces with arbitrarily many connected components.

Findings

Existence of vector bundles on complete intersection surfaces.

Moduli spaces of rank 2 stable bundles can have arbitrarily many connected components.

New construction techniques using hypersurfaces with unexpected linear spaces.

Abstract

We use hypersurfaces containing unexpected linear spaces to construct interesting vector bundles on complete intersection surfaces in projective space. We discover examples of moduli spaces of rank 2 stable bundles on surfaces of Picard rank one with arbitrarily many connected components.