On some Moduli spaces of stable vector bundles on cubic and quartic threefolds

TL;DR

This paper investigates the structure of moduli spaces of stable rank-two vector bundles on cubic and quartic threefolds, revealing their completeness, irreducibility, and cohomological properties in various cases.

Contribution

It provides new results on the irreducibility and cohomological vanishing of moduli spaces of stable vector bundles on specific threefolds.

Findings

Moduli spaces are complete and irreducible in many cases.

General members have vanishing intermediate cohomology.

Most components of the moduli space exhibit these properties.

Abstract

We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing intermediate cohomology. In one case, all except one component of the moduli space has such vector bundles.