Petri map for vector bundles near good bundles

TL;DR

This paper proves that on a generic curve, certain stable vector bundles with specified properties have an injective Petri map, under conditions on degree and genus, indicating generic behavior of these bundles.

Contribution

It establishes the existence of a component of stable vector bundles with injective Petri maps under specific degree and genus conditions, advancing understanding of vector bundle moduli.

Findings

Existence of a component B with stable vector bundles of rank r and degree d

Injectivity of the Petri map for a generic bundle in B

Conditions on degree and genus for the results to hold

Abstract

We show that on a generic curve and under some conditions on the degree and genus, there exists a component B of the locus of stable vector bundles of rank r and degree d with at least k sections of the expected dimension such that for a generic vector bundle E of B, the Petri map is injective.