Transactions of the American Mathematical Society

Author(s): Florian Berchtold; Jürgen Hausen
Journal: Trans. Amer. Math. Soc. 359 (2007), 1205-1252.
MSC (2000): Primary 14C20, 14J45, 14J70, 14M20, 14M25, 14Q15
Posted: October 16, 2006
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Abstract: Given a variety

with a finitely generated total coordinate ring, we describe basic geometric properties of

in terms of certain combinatorial structures living in the divisor class group of

. For example, we describe the singularities, we calculate the ample cone, and we give simple Fano criteria. As we show by means of several examples, the results allow explicit computations. As immediate applications we obtain an effective version of the Kleiman-Chevalley quasiprojectivity criterion, and the following observation on surfaces: a normal complete surface with finitely generated total coordinate ring is projective if and only if any two of its non-factorial singularities admit a common affine neighbourhood.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14C20, 14J45, 14J70, 14M20, 14M25, 14Q15

Florian Berchtold
Affiliation: Mathematisches Institut, Universität Heidelberg, 69221 Heidelberg, Germany
Address at time of publication: Fachbereich Mathematik und Statistik, Universität Konstanz, D-78457 Konstanz, Germany
Email: Florian.Berchtold@uni-konstanz.de

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