Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces

Daniele Arcara; Aaron Bertram; Max Lieblich

Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces

Algebraic Geometry 2007-08-17 v1

Authors: Daniele Arcara , Aaron Bertram , Max Lieblich

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.

Keywords

bridgeland stability conditions moduli spaces of sheaves moduli spaces

Cite

@article{arxiv.0708.2247,
  title  = {Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces},
  author = {Daniele Arcara and Aaron Bertram and Max Lieblich},
  journal= {arXiv preprint arXiv:0708.2247},
  year   = {2007}
}

Comments

33 pages, with appendix by Max Lieblich

Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces

Abstract

Keywords

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