Bridgeland Stability conditions on threefolds I: Bogomolov-Gieseker type inequalities
arXiv:1103.5010
Abstract
We construct new t-structures on the derived category of coherent sheaves on smooth projective threefolds. We conjecture that they give Bridgeland stability conditions near the large volume limit. We show that this conjecture is equivalent to a Bogomolov-Gieseker type inequality for the third Chern character of certain stable complexes. We also conjecture a stronger inequality, and prove it in the case of projective space, and for various examples. Finally, we prove a version of the classical Bogomolov-Gieseker inequality, not involving the third Chern character, for stable complexes.
45 pages, 4 figures. Comments are welcome. v2: Referee comments incorporated. To appear in JAG
References in corpus (8)
- Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
- Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces
- Branes, Bundles and Attractors: Bogomolov and Beyond
- Reider's Theorem and Thaddeus Pairs Revisited
- Stability conditions on K3 surfaces
- Bridgeland Stability conditions on threefolds II: An application to Fujita's conjecture
- Stability conditions and extremal contractions
- Stability conditions and Calabi-Yau fibrations
Cited by in corpus (12)
- Projectivity and Birational Geometry of Bridgeland moduli spaces
- The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds
- Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds II
- Bridgeland Stability conditions on threefolds II: An application to Fujita's conjecture
- Gepner point and strong Bogomolov-Gieseker inequality for quintic 3-folds
- Some examples of tilt-stable objects on threefolds
- Stability conditions and extremal contractions
- A note on Bogomolov-Gieseker type inequality for Calabi-Yau 3-folds
- Torsion pairs and filtrations in abelian categories with tilting objects
- Quintic periods and stability conditions via homological mirror symmetry
- Bridgeland stability conditions on twisted Kummer surfaces
- Stability Conditions and Mirror Symmetry of K3 Surfaces in Attractor Backgrounds