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Bounds for Chern classes of semistable vector bundles on complex projective spaces

Wiera Dobrowolska (1993)

Colloquium Mathematicae

This work concerns bounds for Chern classes of holomorphic semistable and stable vector bundles on n . Non-negative polynomials in Chern classes are constructed for 4-vector bundles on 4 and a generalization of the presented method to r-bundles on n 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.

Bridgeland-stable moduli spaces for K -trivial surfaces

Daniele Arcara, Aaron Bertram (2013)

Journal of the European Mathematical Society

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 𝒪 C ( H ) when H generates Pic ( S ) and C H . If, in addition, S is a K 3 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...

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