Babylonian Tower Theorems on the Punctured Spectrum.
This work concerns bounds for Chern classes of holomorphic semistable and stable vector bundles on . Non-negative polynomials in Chern classes are constructed for 4-vector bundles on and a generalization of the presented method to r-bundles on is given. At the end of this paper the construction of bundles from complete intersection is introduced to see how rough the estimates we obtain are.
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 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...