On the structure of S₂-ifications of complete local rings

2014/01/23 by Sean Sather-Wagstaff, Sather-Wagstaff, Sean, Sandra Spiroff +1
Mathematics · #05C78 #13B22 #13J10 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 05C25 #Secondary 13D45 #math.AC #msc:05C25 #msc:05C78 #msc:13B22 #msc:13D45 #msc:13J10

paper · pdf · doi:10.48550/arxiv.1401.6146

14 pages

arxiv created 2014/01/23 · arxiv updated 2014/01/24

Abstract

Motivated by work of Hochster and Huneke, we investigate several constructions related to the S₂-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 Γ_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 maximal ideals of T is equal to the number of connected components of Γ_R. We further investigate this graph by exhibiting a technique for showing that a given graph G can be realized as one of the form Γ_R.

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