The cohomological Brauer group of a toric variety

Details The cohomological Brauer group of a toric variety The cohomological Brauer group of a toric variety

1992-02-19

arxiv.org/abs/alg-geom/9202019v1

Mathematics

Algebraic Geometry

12 pages, AMS-Latex Version 1.0

Scientific paper

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 $\Bbb R^r$. 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 \'etale cohomology group with coefficients in the sheaf of units of any toric variety $X$. This is the so-called cohomological Brauer group of $X$.

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