Describing toric varieties and their equivariant cohomology

2009/09/30 by Matthias Franz · 23 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic Geometry and Number Theory #Cohomology #Equivariant cohomology #Equivariant map #Geometric and Algebraic Topology #Geometry #Mathematics #Pure mathematics #Quotient #Toric variety #Torsion (gastropod) #Torus #math.AG #math.AT #msc:14M25 #msc:55N91 #msc:57Q15

paper · pdf · doi:10.4064/cm121-1-1

published in Colloquium Mathematicum 121(1), 1-16 (Polish Academy of Sciences) · 13 pages; minor changes

openalex publication_date 2010/01/01 · arxiv created 2010/03/25 · arxiv updated 2010/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact case and draw se

Citations

• Topology of Kempf-Ness sets for algebraic torus actions
• Some examples in toric geometry
• Differential Forms in Algebraic Topology
• Exact cohomology sequences with integral coefficients for torus actions

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