Gepner stability conditions on hypersurface categories

Abstract

We construct numerical Bridgeland stability conditions on the category of graded matrix factorizations of every smooth complex projective hypersurface of degree $d\ge2$. These conditions are of Gepner type $(τ,2/d)$, where $τ$ is the grading shift autoequivalence. By Orlov's theorem, this gives stability conditions of Gepner type on all Calabi--Yau hypersurfaces and on Kuznetsov components of all Fano hypersurfaces. These conditions satisfy a mass-Hom bound and the support property on the full numerical Grothendieck group. Semistable objects of fixed numerical class and phase admit proper good moduli spaces.