The polyhedral Hodge number h²1 and vanishing of obstructions

الأصل · EN

We prove a vanishing theorem for the Hodge number h²1 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 h²1 implies that these deformations are unobstructed.