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2012

On some moduli of complexes on K3 surfaces

Lo, Jason

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We consider moduli stacks of Bridgeland semistable objects that previously had only set-theoretic identifications with Uhlenbeck compactification spaces.

On a K3 surface $X$, we give examples where such a moduli stack is isomorphic to a moduli stack of slope semistable locally free sheaves on the Fourier-Mukai partner $\hat{X}$.
This yields a morphism from the stack of Bridgeland semistable objects to a projective scheme, which induces an injection on closed points.
It also allows us to extend a theorem of Bruzzo-Maciocia on Hilbert schemes to a statement on moduli of complexes.

On some moduli of complexes on K3 surfaces · Around

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T. Bridgeland, Fourier-Mukai transforms for surfaces and moduli spaces of stable sheaves , PhD thesis, University of Edinburgh, 1998
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D. Huybrechts, Derived and Abelian equivalences of K3 surfaces , preprint, 2006. arXiv:math/0604150v1 [math.AG]
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M. Lieblich, Moduli of complexes on a proper morphism , J. Algebraic Geom., Vol. 15, pp. 175-206, 2006
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J. Lo and Z. Qin, Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces , 2011, preprint. arXiv:1103.4352v1 [math.AG]
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A. Maciocia and C. Meachan, Rank one Bridgeland stable moduli spaces on a principally polarised Abelian surface , preprint, 2011. arXiv:1107.5304v1 [math.AG]
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H. Minamide, S. Yanagida and K. Yoshioka, Fourier-Mukai transforms and the wall-crossing behavior for Bridgeland’s stability conditions , preprint, 2011. arXiv:1106.5217v1 [math.AG]
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