Some stable vector bundles with reducible theta divisors

TL;DR

This paper constructs stable vector bundles with reducible theta divisors on algebraic curves, demonstrating their stability and geometric properties for general line bundles of degree 2g.

Contribution

It introduces a new class of stable vector bundles with reducible theta divisors, expanding understanding of their structure on algebraic curves.

Findings

Bundles M and its exterior powers are stable for general line bundles L.

These bundles admit reducible theta divisors.

The construction applies to curves of arbitrary genus g.

Abstract

Let C be a curve of genus g and L a line bundle of degree 2g on C . Let M be the kernel of the evaluation map from the trivial bundle with fibre H^0(C,L) into L . We show that when L is general enough, the rank g bundle M and its exterior powers are stable and admit a reducible theta divisor.