1992/02/19 by Frank DeMeyer, Tim Ford, DeMeyer, Frank +3
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9202019
12 pages, AMS-Latex Version 1.0
arxiv created 1992/02/19 · openalex publication_date 1992/02/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Toric varieties are a special class of rational varieties defined by equations of the form \it monomial = monomial. For a good brief survey of the history and role of toric varieties see [10]. Any toric variety X contains a cover by affine open sets described in terms of arrangements (called fans) of convex bodies in \Bbb Rr. The coordinate rings of each of these affine open sets is a graded ring generated over the ground field by monomials. As a consequence, toric varieties provide a good context in which cohomology can be calculated. The purpose of this article is to describe the second étale cohomology group with coefficients in the sheaf of units of any toric variety X. This is the so-called cohomological Brauer group of X.