Journal of Commutative Algebra

Valuative and geometric characterizations of Cox sheaves

Benjamin Bechtold

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We give an intrinsic characterization of Cox sheaves on Krull schemes in terms of their valuative algebraic properties. We also provide a geometric characterization of their graded relative spectra in terms of good quotients of graded schemes, extending the existing theory on relative spectra of Cox sheaves on normal varieties. Moreover, we obtain an irredundant characterization of Cox rings which, in turn, produces a normality criterion for certain graded rings.

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J. Commut. Algebra, Volume 10, Number 1 (2018), 1-43.

First available in Project Euclid: 18 May 2018

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Zentralblatt MATH identifier

Primary: 13A02: Graded rings [See also 16W50] 13A18: Valuations and their generalizations [See also 12J20] 14A20: Generalizations (algebraic spaces, stacks)

Cox rings Krull schemes graded schemes


Bechtold, Benjamin. Valuative and geometric characterizations of Cox sheaves. J. Commut. Algebra 10 (2018), no. 1, 1--43. doi:10.1216/JCA-2018-10-1-1.

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