Partial semiorthogonal decompositions for quiver moduli

TL;DR

This paper constructs semiorthogonal decompositions of derived categories of quiver moduli spaces by embedding derived categories of quivers and line bundles, utilizing QuiverTools for geometric analysis.

Contribution

It introduces a method to embed derived categories of quivers and line bundles into quiver moduli spaces, initiating semiorthogonal decompositions similar to those for vector bundle moduli.

Findings

Embedded derived categories of quivers into moduli spaces

Established semiorthogonal decompositions for quiver moduli

Developed QuiverTools for geometric computations

Abstract

We embed several copies of the derived category of a quiver and certain line bundles in the derived category of an associated moduli space of representations, giving the start of a semiorthogonal decomposition. This mirrors the semiorthogonal decompositions of moduli of vector bundles on curves. Our results are obtained with QuiverTools, an open-source package of tools for quiver representations, their moduli spaces and their geometrical properties.