A generalized Bogomolov-Gieseker inequality for the three-dimensional projective space

Abstract

A generalized Bogomolov-Gieseker inequality for tilt-stable complexes on a smooth projective threefold was conjectured by Bayer, Toda, and the author. We show that such inequality holds true in general, if it holds true when the polarization is sufficiently small. As an application, we prove it for the three-dimensional projective space.

17 pages, 4 figures

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• Spaces of stability conditions
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Cited by in corpus (33)

• A generalized Bogomolov-Gieseker inequality for the smooth quadric threefold
• Stability conditions in families
• On stability conditions for the quintic threefold
• Counterexample to the Generalized Bogomolov-Gieseker Inequality for Threefolds
• Stability conditions on Fano threefolds of Picard number one
• Stability conditions on product threefolds of projective spaces and Abelian varieties
• Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
• Derived categories and the genus of space curves
• The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds
• Stability conditions on threefolds with nef tangent bundles
• Bridgeland Stability on Blow Ups and Counterexamples
• Some remarks on Fano threefolds of index two and stability conditions
• Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds II
• Derived category of coherent sheaves and counting invariants
• Walls and asymptotics for Bridgeland stability conditions on 3-folds
• 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
• Gepner point and strong Bogomolov-Gieseker inequality for quintic 3-folds
• Bridgeland stability conditions on some threefolds of general type
• Stability conditions on Calabi-Yau double/triple solids
• Stability and Applications
• Families of elliptic curves in ${\mathbb{P}}^3$ and Bridgeland Stability
• Some examples of tilt-stable objects on threefolds
• The genus of projective curves on complete intersection surfaces
• On the Bogomolov-Gieseker inequality for hypersurfaces in the projective spaces
• Hilbert scheme of twisted cubics as simple wall-crossing
• Geometry of canonical genus four curves
• New moduli spaces of one-dimensional sheaves on ${\mathbb{P}}^3$
• Fullness of exceptional collections via stability conditions -- A case study: the quadric threefold
• Stability condition on Calabi-Yau threefold of complete intersection of quadratic and quartic hypersurfaces
• Torsion pairs and filtrations in abelian categories with tilting objects