Intersection Homology of Toric Varieties and a Conjecture of Kalai

1997/04/13 by Tom Braden, Braden, Tom C., Robert MacPherson +1 · 3 citations
Mathematics · #14F32 (primary) 52B05 (secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.alg-geom/9704014

openalex publication_date 1997/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the intersection homology Poincare' polynomial P(X) of an affine toric variety X is bounded below by the product P(Y)P(X/Y), where Y is the closure of any orbit in X and X/Y is a slice transverse to the orbit. This proves a combinatorial conjecture of Kalai for rational polytopes.

Cited by

• Subdivisions of lower Eulerian posets and KLS theory
• Subdivisions of lower Eulerian posets
• Intersection cohomology without spaces

Related

• Remarks on the combinatorial intersection cohomology of fans
• Link Bundles and Intersection Spaces of Complex Toric Varieties
• Intersection Theory on Toric Varieties
• Ring structure, uniform expressions and intersection homology
• Combinatorial Cycle Classes in the Intersection Cohomology of Projective Toric Varieties