Bridgeland-stable moduli spaces for K-trivial surfaces

Abstract

We give a one-parameter 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 OC(H) when H generates Pic(S) and C ∈ |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. © European Mathematical Society 2013.