Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces

Abstract

We give a natural family of Bridgeland stability conditions on the derived category of a smooth projective complex surface S and describe ``wall-crossing behavior'' for objects with the same invariants as $\cO_C(H)$ when H generates Pic(S) and $C\in |H|$. If, in addition, S is a K3 or Abelian surface, we use this description to construct a sequence of fine moduli spaces of Bridgeland-stable objects via Mukai flops and generalized elementary modifications of the universal coherent sheaf. We also discover a natural generalization of Thaddeus' stable pairs for curves embedded in the moduli spaces.

33 pages, with appendix by Max Lieblich

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• Projectivity and Birational Geometry of Bridgeland Moduli spaces on an Enriques Surface
• Fourier-Mukai transforms and the wall-crossing behavior for Bridgeland's stability conditions
• Birational Geometry of Singular Moduli Spaces of O'Grady Type
• Moduli of PT-Semistable Objects I
• Projectivity and Birational Geometry of Bridgeland moduli spaces
• Bridgeland Stability conditions on threefolds I: Bogomolov-Gieseker type inequalities
• Some moduli spaces of Bridgeland's stability conditions
• Reider's Theorem and Thaddeus Pairs Revisited
• The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds
• Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces
• The birational geometry of moduli space of sheaves on the projective plane
• Gepner point and strong Bogomolov-Gieseker inequality for quintic 3-folds
• Bridgeland's stabilities on abelian surfaces
• Wall crossing of the moduli spaces of perverse coherent sheaves on a blow-up
• Stability conditions and extremal contractions
• Fano varieties of cubic fourfolds containing a plane
• Stability and Fourier-Mukai transforms on elliptic fibrations
• A note on Bogomolov-Gieseker type inequality for Calabi-Yau 3-folds
• Moduli of Bridgeland semistable objects on ${\mathbb{P}}^2$
• Chern degree functions
• Stability and Fourier-Mukai Transforms on Higher Dimensional Elliptic Fibrations
• Stable pairs on local K3 surfaces
• Joyce invariants for K3 surfaces and mock theta functions
• Flips of moduli of stable torsion free sheaves with $c_1=1$ on ${\mathbb{P}}^2$