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Twisted Fourier-Mukai transforms for holomorphic symplectic fourfolds

Justin Sawon
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Abstract

We apply the methods of C{ă}ld{ă}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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Justin Sawon. 2005-09-09. Twisted Fourier-Mukai transforms for holomorphic symplectic fourfolds. https://arxiv.org/abs/math/0509222

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