Geometric realizations of quiver algebras

TL;DR

This paper develops a method to construct strong exceptional collections of vector bundles on smooth projective varieties with a specified endomorphism algebra, and explores applications to noncommutative geometry and quiver theory.

Contribution

It provides a universal construction approach for exceptional collections with prescribed endomorphism algebras, extending the understanding of geometric realizations of quiver algebras.

Findings

Construction always has a solution

Applications to noncommutative projective planes

Connections to the 3-point Ising quiver

Abstract

In this paper we construct strong exceptional collections of vector bundles on smooth projective varieties that have a prescribed endomorphism algebra. We prove the construction problem always have a solution. We consider some applications to noncommutative projective planes and to the quiver connected with the 3-point Ising function.