2010/07/13 by Akio Hattori, Hattori, Akio · 1 citation
Mathematics · #14M25 #52B29 #57R91 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #math.AT #msc:14M25 #msc:52B29 #msc:57R91
paper · pdf · doi:10.48550/arxiv.1007.2046
17 pages
arxiv created 2010/07/13 · openalex publication_date 2010/07/13 · arxiv updated 2010/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a complete \Q-factorial toric variety of dimension n and \del the fan in a lattice N associated to X. For each cone σ of \del there corresponds an orbit closure V(σ) of the action of complex torus on X. The homology classes \[V(σ)]| dim σ=k\ form a set of specified generators of Hn-k(X,\Q). It is shown that, given α∈ Hn-k(X,\Q), there is a canonical way to express α as a linear combination of the [V(σ)] with coefficients in the field of rational functions of degree 0 on the Grassmann manifold of (n-k+1)-planes in N_\Q. This generalizes Morelli's formula for α the (n-k)-th component of the Todd homology class of the variety X.