Open Access
2018 Valuative and geometric characterizations of Cox sheaves
Benjamin Bechtold
J. Commut. Algebra 10(1): 1-43 (2018). DOI: 10.1216/JCA-2018-10-1-1


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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Benjamin Bechtold. "Valuative and geometric characterizations of Cox sheaves." J. Commut. Algebra 10 (1) 1 - 43, 2018.


Published: 2018
First available in Project Euclid: 18 May 2018

zbMATH: 06875412
MathSciNet: MR3804845
Digital Object Identifier: 10.1216/JCA-2018-10-1-1

Primary: 13A02 , 13A18 , 14A20

Keywords: Cox rings , graded schemes , Krull schemes

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

Vol.10 • No. 1 • 2018
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