Semiample hypersurfaces in toric varieties

Details Semiample hypersurfaces in toric varieties Semiample hypersurfaces in toric varieties

1998-12-31

arxiv.org/abs/math/9812163v2

Published in Duke Math. J., vol. 101 (2000), pp. 85-116

Mathematics

Algebraic Geometry

Some corrections made (Lemma 5.7, Theorem 5.9)

Scientific paper

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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