Tohoku Mathematical Journal
2000
December
SECOND SERIES VOL. 52, NO. 4

Tohoku Math. J.
52 (2000), 579-602

Title THE POLYHEDRAL HODGE NUMBER $H^{2,1}$ AND VANISHING OF OBSTRUCTIONS

Author Klaus Altmann and Duco van Straten

(Received April 15, 1999, revised January 24, 2000)
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.

2000 Mathematics Subject Classification. Primary 52B20; Secondary 14M25, 13D10, 52B05.

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