Multiple structures with arbitrarily large projective dimension supported on linear subspaces

JOURNAL OF ALGEBRA

卷:447

Article

Huneke, Craig¹  Mantero, Paolo²  McCullough, Jason³  Seceleanu, Alexandra⁴ 

[1] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

[2] Univ Arkansas, Dept Math, Fayetteville, AR 72701 USA

[3] Rider Univ, Dept Math, Lawrenceville, NJ 08648 USA

[4] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

关键词: Multiple structures;    Projective dimension;    Multiplicity;    Primary ideals;    Unmixed ideals;    Free resolution;    Linkage;   

DOI  :  10.1016/j.jalgebra.2015.09.019

来源: Elsevier

【 摘 要 】

Let K be an algebraically closed field. There has been much interest in characterizing multiple structures in P-K(n) defined on a linear subspace of small codimension under additional assumptions (e.g. Cohen-Macaulay). We show that no such finite characterization of multiple structures is possible if one only assumes unmixedness. Specifically, we prove that for any positive integers h, e >= 2 with (h, e) not equal (2,2) and p >= 5 there is a homogeneous ideal I in a polynomial ring over K such that (1) the height of I is h, (2) the Hilbert-Samuel multiplicity of R/I is e, (3) the projective dimension of R/I is at least p and (4) the ideal I is primary to a linear prime (x(1), ..., x(h)). This result is in stark contrast to Manolache's characterization of Cohen-Macaulay multiple structures in codimension 2 and multiplicity at most 4 and also to Engheta's characterization of unmixed ideals of height 2 and multiplicity 2. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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