Existence of vector bundles of rank two with fixed determinant and sections

TL;DR

This paper proves the existence of certain rank-two vector bundles with fixed determinant and a specified number of sections, under particular conditions, contributing to the understanding of their moduli space.

Contribution

It establishes the existence of a component of the expected dimension in the moduli space of stable rank-two vector bundles with fixed determinant and sections, under generic conditions.

Findings

Existence of a component of the expected dimension in B_{2,L}^k.

Results hold under suitable numerical conditions.

Valid for generic line bundles L.

Abstract

Consider the scheme B_{2,L}^k of stable vector bundles of rank two and fixed determinant L which have at least k sections. Under suitable numerical conditions and for generic L, we show the existence of a component of the expected dimension of B_{2,L}^k.