We give a one-parameter family of Bridgeland stability conditions on the derived category of a smooth projective complex surface and describe "wall-crossing behavior'' for objects with the same invariants as when generates Pic and . If, in addition, 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.
Cite this article
Daniele Arcara, Aaron Bertram, Bridgeland-stable moduli spaces for -trivial surfaces. J. Eur. Math. Soc. 15 (2013), no. 1, pp. 1–38DOI 10.4171/JEMS/354