A generalized Bogomolov-Gieseker inequality for the smooth quadric threefold

Abstract

We prove a generalized Bogomolov-Gieseker inequality as conjectured by Bayer, Macrì and Toda for the smooth quadric threefold. This implies the existence of a family of Bridgeland stability conditions.

v1: 10 pages. v2: Updated references. v3: 11 pages. Several minor corrections. Accepted for publication in "Bulletin of the London Mathematical Society"

References in corpus (2)

• A generalized Bogomolov-Gieseker inequality for the three-dimensional projective space
• Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds II

Cited by in corpus (24)

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• On stability conditions for the quintic threefold
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• Stability conditions on Fano threefolds of Picard number one
• Stability conditions on product threefolds of projective spaces and Abelian varieties
• Derived categories and the genus of space curves
• Stability conditions on threefolds with nef tangent bundles
• Moduli of Bridgeland semistable objects on 3-folds and Donaldson-Thomas invariants
• The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds
• Bridgeland Stability on Blow Ups and Counterexamples
• Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds II
• Derived category of coherent sheaves and counting invariants
• Curve counting and S-duality
• T-structures on elliptic fibrations
• The Effective Cone of Moduli Spaces of Sheaves on a Smooth Quadric Surface
• Generalized Bogomolov-Gieseker type inequalities on Fano 3-folds
• Bridgeland stability conditions on some threefolds of general type
• Stability and Applications
• Stability conditions on Calabi-Yau double/triple solids
• Families of elliptic curves in ${\mathbb{P}}^3$ and Bridgeland Stability
• The genus of projective curves on complete intersection surfaces
• New moduli spaces of one-dimensional sheaves on ${\mathbb{P}}^3$
• Stability condition on Calabi-Yau threefold of complete intersection of quadratic and quartic hypersurfaces
• Fullness of exceptional collections via stability conditions -- A case study: the quadric threefold