Closed form expressions for Hodge numbers of complete intersection Calabi-Yau threefolds in toric varieties

Details Closed form expressions for Hodge numbers of complete intersection Calabi-Yau threefolds in toric varieties Closed form expressions for Hodge numbers of complete intersection Calabi-Yau threefolds in toric varieties

2009-07-15

arxiv.org/abs/0907.2701v2

Mirror Symmetry and Tropical Geometry, Contemporary Mathematics, vol. 527, Amer. Math. Soc., Providence, RI, 2010, pp. 1-14

Mathematics

Combinatorics

14 pages, published version

Scientific paper

We use Batyrev-Borisov's formula for the generating function of stringy Hodge numbers of Calabi-Yau varieties realized as complete intersections in toric varieties in order to get closed form expressions for Hodge numbers of Calabi-Yau threefolds in five-dimensional ambient spaces. These expressions involve counts of lattice points on faces of associated Cayley polytopes. Using the same techniques, similar expressions may be obtained for higher dimensional varieties realized as complete intersections of two hypersurfaces.

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