Hodge Spaces for Real Toric Varieties

2007/05/03 by Valerie Hower, Hower, Valerie
Mathematics · #52B12 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Primary 14M25 #Secondary 55T99 #math.AG #math.AT #msc:14M25 #msc:52B12 #msc:55T99

paper · pdf · doi:10.48550/arxiv.0705.0516

22 pages, 2 figures

arxiv created 2007/05/03 · openalex publication_date 2007/05/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

Related

• Fiber fans and toric quotients
• Combinatorial Cycle Classes in the Intersection Cohomology of Projective Toric Varieties
• Spaces of non-resultant systems of real bounded multiplicity determined by a toric variety
• Irrational Toric Varieties
• Sections hyperplanes à singularités simples et exemples de variations de structure de Hodge