An alternating matrix and a vector, with application to Aluffi algebras

JOURNAL OF ALGEBRA

卷:472

Article

Kustin, Andrew R.¹ 

[1] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

关键词: Aluffi algebra;    Bourbaki ideal;    Gorenstein ideal;    Grassmannian;    Maximal Cohen-Macaulay module;    Module of derivations;    Perfect module;    Pfaffians;    Schubert variety;    Self-dual module;    Totally acyclic module;   

DOI  :  10.1016/j.jalgebra.2016.10.005

来源: Elsevier

【 摘 要 】

Let X be a generic alternating matrix, t be a generic row vector, and J be the ideal Pf(4)(X) + I-1(tX). We prove that J is a perfect Gorenstein ideal of grade equal to the grade of Pf(4)(X) plus two. This result is used by Ramos and Simis in their calculation of the Aluffi algebra of the module of derivations of the homogeneous coordinate ring of a smooth projective hypersurface. We also prove that J defines a domain, or a normal ring, or a unique factorization domain if and only if the base ring has the same property. The main object of study in the present paper is the module N which is equal to the column space of X, calculated mod Pf(4)(X). The module N is a self-dual maximal Cohen Macaulay module of rank two; furthermore, J is a Bourbaki ideal for N. The ideals which define the homogeneous coordinate rings of the Plucker embeddings of the Schubert subvarieties of the Grassmannian of planes are used in the study of the module N. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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