Gepner type stability condition via Orlov/Kuznetsov equivalence

TL;DR

This paper establishes Gepner type stability conditions on categories of graded matrix factorizations linked to cubic fourfolds with a plane, using Orlov/Kuznetsov equivalence and Clifford algebra sheaves.

Contribution

It introduces a novel approach to constructing Gepner type stability conditions via Orlov/Kuznetsov equivalence and Clifford algebra sheaves for specific cubic fourfolds.

Findings

Existence of Gepner type stability conditions proven

Description of grade shift functor via Clifford algebra sheaves

Application to cubic fourfolds containing a plane

Abstract

We show the existence of Gepner type Bridgeland stability conditions on the triangulated categories of graded matrix factorizations associated with homogeneous polynomials which define general cubic fourfolds containing a plane. The key ingredient is to describe the grade shift functor of matrix factorizations in terms of sheaves of Clifford algebras on the projective plane under Orlov/Kuznetsov equivalence.