Twisted Fourier-Mukai transforms for holomorphic symplectic fourfolds

Details Twisted Fourier-Mukai transforms for holomorphic symplectic fourfolds Twisted Fourier-Mukai transforms for holomorphic symplectic fourfolds

2005-09-09

arxiv.org/abs/math/0509222v1

Adv. Math. 218 (2008), no. 3, 828-864

Mathematics

Algebraic Geometry

40 pages

Scientific paper

We apply the methods of C{\u{a}}ld{\u{a}}raru to construct a twisted Fourier-Mukai transform between a pair of holomorphic symplectic four-folds. More precisely, we obtain an equivalence between the derived category of coherent sheaves on a certain four-fold and the derived category of twisted sheaves on its `mirror' partner. As corollaries, we show that the two spaces are connected by a one-parameter family of deformations through Lagrangian fibrations, and we extend the original Fourier-Mukai transform to degenerations of abelian surfaces.

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