Towards mirror symmetry for varieties of general type

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• Helge Ruddat (Mainz)
• Wednesday 18 January 2012, 14:15-15:15
• MR4, CMS.

If you have a question about this talk, please contact Ivan Smith.

Assuming the natural compactification X of a hypersurface in an affine algebraic torus is smooth, it can exhibit any Kodaira dimension depending on the size and shape of the Newton polyhedron of X. In a joint work with Mark Gross and Ludmil Katzarkov, we give a construction for the expected mirror symmetry partner of a complete intersection X in a toric variety which works for any Kodaira dimension of X. The mirror dual might be reducible and is equipped with a sheaf of vanishing cycles. We give evidence for the duality by proving the symmetry of the Hodge numbers when X is a hypersurface. The leading example will be the mirror of a genus two curve. If time permits, I will explain relations to homological mirror symmetry and the Gross-Siebert construction.

This talk is part of the Algebraic Geometry Seminar series.

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