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This article is cited in 47 scientific papers (total in 47 papers)
Cox Rings and Combinatorics II
J. Hausen Mathematisches Institut, Universität Tübingen
Abstract:
We study varieties with a finitely generated Cox ring. In the first part, we generalize a combinatorial approach developed in earlier work for varieties with a torsion free divisor class group to the case of torsion. Then we turn to modifications, e.g., blow-ups, and the question how the Cox ring changes under such maps. We answer this question for a certain class of modifications induced from modifications of ambient toric varieties. Moreover, we show that every variety with finitely generated Cox ring can be explicitly constructed in a finite series of toric ambient modifications from a combinatorially minimal one.
Key words and phrases:
Cox ring, total coordinate ring, divisors, modifications.
Received: January 26, 2008
Citation:
J. Hausen, “Cox Rings and Combinatorics II”, Mosc. Math. J., 8:4 (2008), 711–757
Linking options:
https://www.mathnet.ru/eng/mmj327 https://www.mathnet.ru/eng/mmj/v8/i4/p711
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