Petri map for rank two bundles with canonical determinant

TL;DR

This paper proves a conjecture related to the injectivity of the Petri-canonical map for rank two vector bundles with canonical determinant on a generic curve, advancing understanding in algebraic geometry.

Contribution

It establishes the Bertram-Feinberg-Mukai conjecture for generic curves and semistable rank two bundles with canonical determinant.

Findings

Proves injectivity of the Petri-canonical map for the specified bundles.

Confirms the conjecture for generic curves of any genus.

Enhances understanding of vector bundle properties on algebraic curves.

Abstract

We prove the Bertram-Feinberg-Mukai conjecture for a generic curve $C$ of genus $g$ and a semistable vector bundle $E$ of rank two and determinant $K$ on $C$, namely we prove the injectivity of the Petri-canonical map $S^2(H^0(E))\to H^0(S^2(E))$.