Rank four vector bundles without theta divisor over a curve of genus two

TL;DR

This paper explores the relationship between stable rank four vector bundles without theta divisor and theta-characteristics over genus two curves, providing descriptions and degree computations of related maps.

Contribution

It establishes a canonical bijection between these vector bundles and theta-characteristics, offering new insights and descriptions in the context of algebraic geometry.

Findings

Bijection between vector bundles and theta-characteristics

Descriptions of these vector bundles

Degree computation of the theta map

Abstract

We show that the locus of stable rank four vector bundles without theta divisor over a smooth projective curve of genus two is in canonical bijection with the set of theta-characteristics. We give several descriptions of these bundles and compute the degree of the rational theta map.