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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...

Bubble tree compactification of moduli spaces of vector bundles on surfaces

Dimitri Markushevich, Alexander Tikhomirov, Günther Trautmann (2012)

Open Mathematics

We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundles and connections in differential geometry. The new moduli spaces are algebraic spaces arising as quotients by group actions according to a result of Kollár. As an example, the compactification of the space of stable rank 2 vector bundles with Chern classes c 1 = 0, c 1...

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