## Tohoku Mathematical Journal

### The polyhedral Hodge number $h^{2,1}$ and vanishing of obstructions

#### Abstract

We prove a vanishing theorem for the Hodge number $h^{2,1}$ of projective toric varieties provided by a certain class of polytopes. We explain how this Hodge number also gives information about the deformation theory of the toric Gorenstein singularity derived from the same polytope. In particular, the vanishing theorem for $h^{2,1}$ implies that these deformations are unobstructed.

#### Article information

Source
Tohoku Math. J. (2), Volume 52, Number 4 (2000), 579-602.

Dates
First available in Project Euclid: 3 May 2007

https://projecteuclid.org/euclid.tmj/1178207756

Digital Object Identifier
doi:10.2748/tmj/1178207756

Mathematical Reviews number (MathSciNet)
MR1793937

Zentralblatt MATH identifier
1017.52005

#### Citation

Altmann, Klaus; van Straten, Duco. The polyhedral Hodge number $h^{2,1}$ and vanishing of obstructions. Tohoku Math. J. (2) 52 (2000), no. 4, 579--602. doi:10.2748/tmj/1178207756. https://projecteuclid.org/euclid.tmj/1178207756

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