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A Barth-Lefschetz theorem for toric varieties

Joerg Zintl
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Abstract

The theorem of Barth-Lefschetz is a statement about the cohomology of a submanifold X of some projective space, in a range depending on the codimension of the embedding. Here this is generalized to the case of a submanifold X of a smooth projective toric variety Y, under some natural conditions on X. In particular, in the Barth-Lefschetz range a formula for the Hodge numbers of X in terms of the toric, i.e. combinatorial data of Y is given.

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Joerg Zintl. 2002-06-06. A Barth-Lefschetz theorem for toric varieties. https://arxiv.org/abs/math/0112198

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