877 research outputs found
Normal bundles to Laufer rational curves in local Calabi-Yau threefolds
We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear
deformation of a rank 2 holomorphic vector bundle on a smooth rational curve,
such that X has trivial canonical bundle and has sections. Then the normal
bundle to such sections is computed in terms of the rank of the Hessian of a
suitably defined superpotential at its critical points
A Fourier transform for sheaves on Lagrangian families of real tori
We systematically develop a transform of the Fourier-Mukai type for sheaves
on symplectic manifolds of any dimension fibred in Lagrangian tori. One
obtains a bijective correspondence between unitary local systems supported on
Lagrangian submanifolds of and holomorphic vector bundles with compatible
unitary connections supported on complex submanifolds of the relative Jacobian
of (suitable conditions being verified on both sides).Comment: Latex, 30 pages (in a4wide format), no figures. v2: Minor expository
changes, typos corrected. v3: Final version to appear in two parts in J.
Geom. Phy
Categorial mirror symmetry for K3 surfaces
We study the structure of a modified Fukaya category
associated with a K3 surface , and prove that whenever is an elliptic K3
surface with a section, the derived category of \fF(X) is equivalent to a
subcategory of the derived category of coherent sheaves on
the mirror K3 surface .Comment: 11 pages, AmsLatex. Exposition (hopefully) improved, one argument
simplifie
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