1995/05/24 by Timothy J. Ford, Ford, Timothy J.
Computer Science · Mathematics · #14F20 (Secondary) #14M25 (Primary) 13A20 #16A16 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #alg-geom #math.AC #math.AG #msc:13A20 #msc:14F20 #msc:14M25 #msc:16A16
paper · pdf · doi:10.48550/arxiv.alg-geom/9505025
16 pages with 2 figures, Author-supplied DVI file available at ftp://ftp.math.fau.edu/pub/Ford/itv.dvi, Author-supplied PostScript file available at ftp://ftp.math.fau.edu/pub/Ford/itv.ps, AMSLaTeX v 1.2
arxiv created 1995/05/24 · openalex publication_date 1995/05/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Associated to a toric variety X of dimension r over a field k is a fan Δ on \Bbb Rr. The fan Δ is a finite set of cones which are in one-to-one correspondence with the orbits of the torus action on X. The fan Δ inherits the Zariski topology from X. In this article some cohomological invariants of X are studied in terms of whether or not they depend only on Δ and not k. Secondly some numerical invariants of X are studied in terms of whether or not they are topological invariants of the fan Δ. That is, whether or not they depend only on the finite topological space defined on Δ. The invariants with which we are mostly concerned are the class group of Weil divisors, the Picard group, the Brauer group and the dimensions of the torsion free part of the étale cohomology groups with coefficients in the sheaf of units. The notion of an open neighborhood of a fan is introduced and examples are given for which the above invariants are sufficiently fine to give nontrivial stratifications of an open neighborhood of a fan all of whose maximal cones are nonsimplicial.