Thick Subcategories of Discrete Derived Categories

TL;DR

This paper classifies thick subcategories of discrete derived categories using geometric arc-collections, revealing their structure, classification, and mutation dynamics, thus advancing understanding of their algebraic and geometric properties.

Contribution

Introduces arc-collections as generators for thick subcategories and describes their topological classification and mutation behavior.

Findings

Every thick subcategory is generated by an arc-collection.

Thick subcategories are classified by the topology of arc configurations.

Mutation acts transitively on arc-collections within a subcategory.

Abstract

We classify the thick subcategories of discrete derived categories. To do this we introduce certain generating sets called arc-collections which correspond to configurations of non-crossing arcs on a geometric model. We show that every thick subcategory is generated by an arc-collection, each thick subcategory is determined by the topology of the corresponding configuration, and we describe a version of mutation which acts transitively on the set of arc-collections generating a given thick subcategory.