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2018 On the structure of $S_2$-ifications of complete local rings
Sean Sather-Wagstaff, Sandra Spiroff
Rocky Mountain J. Math. 48(3): 947-965 (2018). DOI: 10.1216/RMJ-2018-48-3-947

Abstract

Motivated by work of Hochster and Huneke, we investigate several constructions related to the $S_2$-ification $T$ of a complete equidimensional local ring $R$: the canonical module, the top local cohomology module, topological spaces of the form $Spec (R)-V(J)$, and the (finite simple) graph $\Gamma _R$ with vertex set $Min (R)$ defined by Hochster and Huneke. We generalize one of their results by showing, e.g., that the number of connected components of $\Gamma _R$ is equal to the maximum number of connected components of $Spec (R)-V(J)$ for all $J$ of height $2$. We further investigate this graph by exhibiting a technique for showing that certain graphs $G$ can be realized in the form $\Gamma _R$.

Citation

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Sean Sather-Wagstaff. Sandra Spiroff. "On the structure of $S_2$-ifications of complete local rings." Rocky Mountain J. Math. 48 (3) 947 - 965, 2018. https://doi.org/10.1216/RMJ-2018-48-3-947

Information

Published: 2018
First available in Project Euclid: 2 August 2018

zbMATH: 06917356
MathSciNet: MR3835581
Digital Object Identifier: 10.1216/RMJ-2018-48-3-947

Subjects:
Primary: 05C25, 05C78, 13B22
Secondary: 13D45, 13J10

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 3 • 2018
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