Hypergeometric Equations and Weighted Projective Spaces

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We compute the Hodge numbers of the variation of Hodge structure of the middle cohomology (with compact support) of the Landau-Ginzburg model dual to a weighted projective space. We state a conjectural formula for the Hodge numbers of general hypergeometric variations. We show that a general Landau-Ginzburg fibre is birational to a Calabi-Yau variety if and only if a general anticanonical section of the weighted projective space is Calabi-Yau. We analyse the 104 weighted 3-spaces with canonical singularities, and show that a general anticanonical section is not a K3 surface exactly in those 9 cases where a generic Landau-Ginzburg fibre is an elliptic surface of Kodaira dimension 1.
24 pages

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Algebraic Geometry, 14-xx

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http://salesiana.dossiersoluciones.com/handle/123456789/114113

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0607016
 http://arxiv.org/abs/math/0607016

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arXiv