Kuznetsov Categories for Gauged Linear Sigma Models

TL;DR

This paper introduces Kuznetsov and anti-Kuznetsov categories for gauged linear sigma models, establishing their properties and relations to Fano varieties, and demonstrating their role in describing derived categories of complete intersections.

Contribution

It defines new categorical invariants for gauged linear sigma models and links them to Fano varieties via derived category equivalences.

Findings

Kuznetsov categories are orthogonal to exceptional collections in certain toric varieties.

Complete intersections of ample divisors in Fano GIT quotients are Fano visitors.

Derived categories of these intersections are equivalent to anti-Kuznetsov categories.

Abstract

We define Kuznetsov and anti-Kuznetsov categories for gauged linear sigma models. We show that for complete intersections of ample divisors in smooth projective toric varieties, the Kuznetsov category is left orthogonal to an exceptional collection. We prove that any complete intersection of $r \ge 2$ ample divisors in a Fano GIT quotient is a Fano visitor and the derived category of its Fano host is equivalent to an anti-Kuznetsov category of a gauged linear sigma model.