Injectivity of the Petri map for twisted Brill-Noether loci

TL;DR

This paper proves the injectivity of the twisted Petri map for generic curves and vector bundles, advancing understanding in twisted Brill-Noether theory and its geometric implications.

Contribution

It establishes the injectivity of the twisted Petri map for generic curves and vector bundles, a new result in the study of twisted Brill-Noether loci.

Findings

Injectivity of the twisted Petri map for generic curves and bundles.

Implications for the geometry of twisted Brill-Noether loci.

Advancement in understanding the structure of vector bundles on curves.

Abstract

Let C be a generic curve, E a generic vector bundle on C. Then, for every line bundle on C the twisted Petri map P:H^0(C,L\otimes E)\otimes H^0(C, K\otimes L^*\otimes E^{*})--> H^0(C, K) is injective.