Vector bundles on projective varieties and representations of quivers

TL;DR

This paper establishes equivalences between categories of special vector bundles on projective varieties and certain quiver representations, providing new tools for analyzing their structure and decomposability.

Contribution

It introduces novel categorical equivalences linking vector bundles and quiver representations, and offers criteria for bundle decomposability.

Findings

Categories of cokernel, Steiner, syzygy bundles, and monads are equivalent to quiver representations.

Provides decomposability criteria for these vector bundles.

Establishes a framework for analyzing vector bundles via quiver theory.

Abstract

We present equivalences between certain categories of vector bundles on projective varieties, namely cokernel bundles, Steiner bundles, syzygy bundles, and monads, and full subcategories of representations of certain quivers. As an application, we provide decomposability criteria for such bundles.