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Hypergeometric Equations and Weighted Projective Spaces

Alessio Corti·Vasily Golyshev
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Abstract

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.

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Alessio Corti, Vasily Golyshev. 2006-07-03. Hypergeometric Equations and Weighted Projective Spaces. https://arxiv.org/abs/math/0607016

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