Twisted Fourier-Mukai transforms for holomorphic symplectic four-folds |
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Authors: | Justin Sawon |
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Affiliation: | Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA |
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Abstract: | We apply the methods of C a?ld?raru to construct a twisted Fourier-Mukai transform between a pair of holomorphic symplectic four-folds which are fibred by Lagrangian abelian surfaces. More precisely, we obtain an equivalence between the derived category of coherent sheaves on a certain Lagrangian fibration and the derived category of twisted sheaves on its ‘mirror’ partner. As a corollary, we extend the original Fourier-Mukai transform to degenerations of abelian surfaces. Another consequence of the general theory is that the holomorphic symplectic four-fold and its mirror are connected by a one-parameter family of deformations through Lagrangian fibrations. |
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Keywords: | 14J60 14D06 18E30 53C26 |
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