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Semiample hypersurfaces in toric varieties

Anvar R. Mavlyutov
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Abstract

We study the geometry and cohomology of semiample hypersurfaces in toric varieties. Such hypersurfaces generalize the MPCP-desingularizations of Calabi-Yau ample hypersurfaces in the Batyrev mirror construction. We study the topological cup product on the middle cohomology of semiample hypersurfaces. In particular, we obtain a complete algebraic description of the middle cohomology of regular semiample hypersurfaces in 4-dimensional simplicial toric varieties what would be interesting for physics.

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Anvar R. Mavlyutov. 2000-01-30. Semiample hypersurfaces in toric varieties. https://arxiv.org/abs/math/9812163

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