Klaus Altmann, van Straten Duco
The polyhedral Hodge number h^2,1 and vanishing of obstructions
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

 52B05 Combinatorial properties (number of faces, shortest paths, etc.), See also {05Cxx}

14M25 Toric varieties, Newton polyhedra

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.
Keywords: Convex polytopes, cohomological systems, obstructions.