Ramification and Discriminants of Vector Bundles and a Quick Proof of Bogomolov's Theorem

TL;DR

This paper analyzes degeneracy loci in projectivized vector bundles to compute discriminant degrees and offers a new, streamlined proof of Bogomolov's instability theorem, advancing understanding of vector bundle properties.

Contribution

It introduces a novel approach using degeneracy loci analysis to rederive the degree of discriminants and provides a simplified proof of Bogomolov's theorem.

Findings

Recomputed discriminant degrees using degeneracy loci

Provided a new proof of Bogomolov's instability theorem

Enhanced understanding of vector bundle degeneracy properties

Abstract

By analyzing degeneracy loci over projectivized vector bundles, we recompute the degree of the discriminant locus of a vector bundle and provide a new proof of the Bogomolov instability theorem.