Vector bundles and monads on abelian threefolds

TL;DR

This paper constructs and analyzes stable rank 2 vector bundles on abelian threefolds, using monads and Serre construction, and describes a component of their moduli space.

Contribution

It introduces a monad-based approach to study vector bundles on abelian threefolds and provides a birational description of a moduli space component.

Findings

Computed the dimension of first order deformations

Provided examples of stable vector bundles

Described a 13-dimensional moduli space component

Abstract

We give examples of stable rank 2 vector bundles on principally polarized abelian threefolds, and study their deformations. The starting point is the Serre construction, which gives a source of examples, and which we rephrase in terms of Barth--Hulek like monads. Using the monad description, we compute the dimension of the space of first order infinitesimal deformations of these bundles. Moreover, we obtain a birational description of a 13-dimensional component of the moduli space for stable vector bundles.