Resumen de Twisted Fourier�Mukai transforms for holomorphic symplectic four-folds

Justin Sawon

• We apply the methods of C a?ldararu 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