2005/10/11 by Frédéric Bihan, Matthias Franz, Clint McCrory +2 · 9 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Algebraic geometry #Algebraic number #Algebraic variety #Betti number #Combinatorics #Commutative Algebra and Its Applications #Dimension (graph theory) #Gravitational singularity #Invertible matrix #Mathematical analysis #Mathematics #Number theory #Pure mathematics #Resolution of singularities #Schubert variety #Singular point of an algebraic variety #Toric variety #Variety (cybernetics) #math.AG #math.AT #msc:14P25 #msc:55M35 #msc:55N91
paper · pdf · doi:10.1007/s00229-006-0004-z
published in manuscripta mathematica 120(2), 217-232 (Springer Science+Business Media) · 13 pages
arxiv created 2005/10/11 · openalex publication_date 2006/04/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A complex algebraic variety X defined over the real numbers is called an M-variety if the sum of its Betti numbers (for homology with closed supports and coefficients in Z/2) coincides with the corresponding sum for the real part of X. It has been known for a long time that any nonsingular complete toric variety is an M-variety. In this paper we consider whether this remains true for toric varieties that are singular or not complete, and we give a positive answer when the dimension of X is less than or equal to 3.