Gepner point and strong Bogomolov-Gieseker inequality for quintic 3-folds

Abstract

We propose a conjectural stronger version of Bogomolov-Gieseker inequality for stable sheaves on quintic 3-folds. Our conjecture is derived from an attempt to construct a Bridgeland stability condition on graded matrix factorizations, which should correspond to the Gepner point via mirror symmetry and Orlov equivalence. We prove our conjecture in the rank two case.

19 pages, a reference is added

References in corpus (4)

• A generalized Bogomolov-Gieseker inequality for the three-dimensional projective space
• Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces
• Matrix Factorizations and Representations of Quivers I
• Gepner type stability conditions on graded matrix factorizations

Cited by in corpus (4)

• The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds
• Derived category of coherent sheaves and counting invariants
• Global dimension function on stability conditions and Gepner equations
• Gepner type stability condition via Orlov/Kuznetsov equivalence