Klaus Altmann, van Straten Duco
The polyhedral Hodge number h2,1 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 h2,1 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 h2,1 implies that these deformations are
unobstructed.
Keywords: Convex polytopes, cohomological systems, obstructions.