Non-Fine Moduli Spaces of Sheaves on K3 Surfaces

By Andrei Căldăraru. 2001

46 citations recorded by the source corpus.

In general, if M is a moduli space of stable sheaves on X, there is a unique alpha in the Brauer group of M such that a pi_M^* alpha^{-1}-twisted universal sheaf exists on X times M. In this paper we study the situation when X and M are K3 surfaces, and we identify alpha in terms of Mukai's map between the cohomology of X and of M (defined by means of a quasi-universal sheaf). We prove that the derived category of sheaves on X and the derived category of alpha-twisted sheaves on M are equivalent. This suggests a conjecture which describes, in terms of Hodge isometries of lattices, when derived categories of twisted sheaves on two K3 surfaces are equivalent. If proven true, this conjecture would generalize a theorem of Orlov and a recent result of Donagi-Pantev.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2ed53677e0404de4d64a8a4c252baf7dc5daa787

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In Geometry and Topology

1. Alberto Canonaco
2. P. Stellari
3. D. Huybrechts
4. Emanuele Macrì
5. Alexander Kuznetsov
6. Arend Bayer

In Mathematical Physics

1. Alberto Canonaco
2. P. Stellari
3. D. Huybrechts
4. Emanuele Macrì
5. Alexander Kuznetsov
6. Arend Bayer

Citations in the corpus

• Twisted Fourier–Mukai functors (2006, methodology): “This was first proved by Căldăraru ([3, 4]) and then generalized in [12, 13, 17] and [9, 10].”