Apery and micro-invariants of a one-dimensional Cohen-Macaulay local ring and invariants of its tangent cone

JOURNAL OF ALGEBRA

卷:328

Article

Cortadellas, Teresa¹  Zarzuela, Santiago¹ 

[1] Univ Barcelona, Dept Algebra & Geometria, E-08007 Barcelona, Spain

关键词: Commutative algebra;    Tangent cone;    Cohen-Macaulay rings;    Neighborhood ring;    Value semigroup;   

DOI  :  10.1016/j.jalgebra.2010.08.002

来源: Elsevier

【 摘 要 】

Given a one-dimensional equicharacteristic Cohen-Macaulay local ring A. Juan Elias introduced in 2001 the set of micro-invariants of A in terms of the first neighborhood ring. On the other hand, if A is a one-dimensional complete equicharacteristic and residually rational domain, Valentina Barucci and Ralf Froberg defined in 2006 a new set of invariants in terms of the Apery set of the value semigroup of A. We give a new interpretation for these sets of invariants that allow to extend their definition to any one-dimensional Cohen-Macaulay ring. We compare these two sets of invariants with the one introduced by the authors for the tangent cone of a one-dimensional Cohen-Macaulay local ring and give explicit formulas relating them. We show that, in fact, they coincide if and only if the tangent cone G(A) is Cohen-Macaulay. Some explicit computations will also be given. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free