Bridgeland-stable moduli spaces for KK-trivial surfaces

  • Daniele Arcara

    Saint Vincent College, Latrobe, USA
  • Aaron Bertram

    University of Utah, Salt Lake City, USA


We give a one-parameter family of Bridgeland stability conditions on the derived category of a smooth projective complex surface SS and describe "wall-crossing behavior'' for objects with the same invariants as OC(H)\mathcal O_C(H) when HH generates Pic(S)(S) and CHC \in |H|. If, in addition, SS 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 KK-trivial surfaces. J. Eur. Math. Soc. 15 (2013), no. 1, pp. 1–38

DOI 10.4171/JEMS/354