Twisted Fourier-Mukai transforms for holomorphic symplectic fourfolds
Algebraic Geometry
2009-04-03 v1
Abstract
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.
Cite
@article{arxiv.math/0509222,
title = {Twisted Fourier-Mukai transforms for holomorphic symplectic fourfolds},
author = {Justin Sawon},
journal= {arXiv preprint arXiv:math/0509222},
year = {2009}
}
Comments
40 pages