Generalized Bogomolov-Gieseker type inequalities on Fano 3-folds

Abstract

We modify the conjectural Bogomolov-Gieseker type inequality introduced by Bayer, Macri and Toda to construct a family of geometric Bridgeland stability conditions on smooth projective 3-folds. We give an equivalent conjecture which needs to check these inequalities for a small class of tilt stable objects. We extend some of the techniques in Li's work for Fano 3-folds of Picard rank one to establish our modified Bogomolov-Gieseker type inequality conjecture for general Fano 3-folds.

Withdrawn for now due to an error in Lemma 5.4 which affects essentially the rest of the paper

References in corpus (2)

• Stability conditions on Fano threefolds of Picard number one
• Moduli of Bridgeland semistable objects on 3-folds and Donaldson-Thomas invariants

Cited by in corpus (4)

• Stability conditions on Kuznetsov components
• Stability conditions on product threefolds of projective spaces and Abelian varieties
• Some remarks on Fano threefolds of index two and stability conditions
• Stability condition on Calabi-Yau threefold of complete intersection of quadratic and quartic hypersurfaces