Bridgeland-stable moduli spaces for \(K\)-trivial surfaces

DOI10.4171/JEMS/354zbMATH Open1259.14014arXiv0708.2247OpenAlexW3100090542MaRDI QIDQ1932203

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Publication date: 17 January 2013

Published in: (Search for Journal in Brave)

Abstract: We give a natural 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 $c{O}_C(H)$ when H generates Pic(S) and $Cin|H|$. 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.

Full work available at URL: https://arxiv.org/abs/0708.2247

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