872 research outputs found

    Normal bundles to Laufer rational curves in local Calabi-Yau threefolds

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    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

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    We systematically develop a transform of the Fourier-Mukai type for sheaves on symplectic manifolds XX of any dimension fibred in Lagrangian tori. One obtains a bijective correspondence between unitary local systems supported on Lagrangian submanifolds of XX and holomorphic vector bundles with compatible unitary connections supported on complex submanifolds of the relative Jacobian of XX (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

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    We study the structure of a modified Fukaya category F(X){\frak F}(X) associated with a K3 surface XX, and prove that whenever XX is an elliptic K3 surface with a section, the derived category of \fF(X) is equivalent to a subcategory of the derived category D(X^){\bold D}(\hat X) of coherent sheaves on the mirror K3 surface X^\hat X.Comment: 11 pages, AmsLatex. Exposition (hopefully) improved, one argument simplifie
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