Moduli spaces of twisted sheaves on a projective variety

We construct the moduli of twisted sheaves on a projective variety. Then we generalize known results on the moduli space of usual sheaves on a K3 surface to the twisted case. Thus we consider the non-emptyness, the deformation type and the Fourier-Mukai transformation. As an application of our results, Daniel Huybrechts and Paolo Stellari prove Caldararu's conjecture.

[1]  D. Huybrechts,et al.  Proof of Caldararu's conjecture. An appendix to a paper by Yoshioka , 2004, math/0411541.

[2]  Max Lieblich.  Moduli of twisted sheaves , 2004, math/0411337.

[3]  N. Hoffmann,et al.  Moduli schemes of rank one Azumaya modules , 2004 .

[4]  A. Langer.  Moduli spaces of sheaves in mixed characteristic , 2004 .

[5]  D. Huybrechts,et al.  Equivalences of twisted K3 surfaces , 2004, math/0409030.

[6]  A. J. Jong.  The period-index problem for the Brauer group of an algebraic surface , 2004 .

[7]  D. Huybrechts,et al.  The Brauer group of analytic K3 surfaces , 2003, math/0305101.

[8]  K. Yoshioka.  Twisted stability and Fourier-Mukai transform II , 2003 .

[9]  K. Yoshioka.  Twisted Stability and Fourier–Mukai Transform I , 2001, Compositio Mathematica.

[10]  S. Mukai.  Vector Bundles on a K3 Surface , 2003, math/0304303.

[11]  A. Căldăraru.  Non-Fine Moduli Spaces of Sheaves on K3 Surfaces , 2001, math/0108180.

[12]  K. Yoshioka.  Moduli spaces of stable sheaves on abelian surfaces , 2000, math/0009001.

[13]  A. Căldăraru.  Derived Categories of Twisted Sheaves on Calabi-Yau Manifolds , 2000 .

[14]  T. Bridgeland.  Equivalences of Triangulated Categories and Fourier–Mukai Transforms , 1998, math/9809114.

[15]  D. Huybrechts,et al.  The geometry of moduli spaces of sheaves , 1997 .

[16]  D. Orlov,et al.  Equivalences of derived categories and K3 surfaces , 1996, alg-geom/9606006.

[17]  Carlos Simpson,et al.  Moduli of representations of the fundamental group of a smooth projective variety I , 1994 .

[18]  S. Mukai.  Symplectic structure of the moduli space of sheaves on an abelian or K3 surface , 1984 .

[19]  向井 茂.  Duality between D(X) and D(X) with its application to Picard sheaves , 1982 .