Hodge Spaces for Real Toric Varieties
Algebraic Geometry
2007-05-23 v1 Algebraic Topology
Abstract
We define the Z/2Z Hodge spaces H_{pq}(\Sigma) of a fan \Sigma. If \Sigma is the normal fan of a reflexive polytope \Delta then we use polyhedral duality to compute the Z/2Z Hodge Spaces of \Sigma. In particular, if the cones of dimension at most e in the face fan \Sigma^* of \Delta are smooth then we compute H_{pq}(\Sigma) for p<e-1. If \Sigma^* is a smooth fan then we completely determine the spaces H_{pq}(\Sigma) and we show the toric variety X associated to \Sigma is 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).
Keywords
Cite
@article{arxiv.0705.0516,
title = {Hodge Spaces for Real Toric Varieties},
author = {Valerie Hower},
journal= {arXiv preprint arXiv:0705.0516},
year = {2007}
}