Hodge Spaces for Real Toric Varieties
arXiv:0705.0516
Abstract
We define the Z/2Z Hodge spaces H_{pq}(Σ) of a fan Σ. If Σis the normal fan of a reflexive polytope Δthen we use polyhedral duality to compute the Z/2Z Hodge Spaces of Σ. In particular, if the cones of dimension at most e in the face fan Σ^* of Δare smooth then we compute H_{pq}(Σ) for p<e-1. If Σ^* is a smooth fan then we completely determine the spaces H_{pq}(Σ) and we show the toric variety X associated to Σis maximal, meaning that the sum of the Z/2Z Betti numbers of X(R) is equal to the sum of the Z/2Z Betti numbers of X(C).
22 pages, 2 figures