A Barth-Lefschetz theorem for toric varieties

Details A Barth-Lefschetz theorem for toric varieties A Barth-Lefschetz theorem for toric varieties

2001-12-19

arxiv.org/abs/math/0112198v2

Math. Z. 242, 415-426 (2002)

Mathematics

Algebraic Geometry

One footnote and one reference added to the published version; 14 pages

Scientific paper

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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