 
Summary: The polyhedral Hodge number h 2;1
and vanishing of obstructions
Klaus Altmann Duco van Straten
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.
1 Introduction
(1.1) For an arbitrary polytope , Brion has introduced in [Br] certain invariants h p;q ().
These are dened as dimensions of cohomology groups H p;q of complexes which are associated
directly to the normal fan of the polytope . In case that is a rational polytope, these invariants
are exactly the Hodge numbers dim H p (IP
();
q
IP () ) with IP () being the projective toric variety
associated to
and
q
