Boundary and shape of Cohen-Macaulay cone

2014/12/05 by Hailong Dao, Dao, Hailong, Kazuhiko Kurano +1
Mathematics · #13D07 #13D15 #13D22 #14C17 #14C35 #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AC #math.KT #msc:13D07 #msc:13D15 #msc:13D22 #msc:14C17 #msc:14C35

paper · pdf · doi:10.48550/arxiv.1412.2182

arxiv created 2014/12/05 · arxiv updated 2014/12/09

Abstract

Let R be a Cohen-Macaulay local domain. In this paper we study the cone of Cohen-Macaulay modules inside the Grothendieck group of finitely generated R-modules modulo numerical equivalences, introduced in \citeCK. We prove a result about the boundary of this cone for Cohen-Macaulay domain admitting de Jong's alterations, and use it to derive some corollaries on finiteness of isomorphism classes of maximal Cohen-Macaulay ideals. Finally, we explicitly compute the Cohen-Macaulay cone for certain isolated hypersurface singularities defined by ξη- f(x₁, …, x_n).

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