The relation type of affine algebras and algebraic varieties

JOURNAL OF ALGEBRA

卷:441

Article

Planas-Vilanova, Francesc

关键词: Relation type;    Rees algebra;    Andre-Quillen homology;   

DOI  :  10.1016/j.jalgebra.2015.07.019

来源: Elsevier

【 摘 要 】

We introduce the notion of relation type of an affine algebra and prove that it is well defined by using the Jacobi-Zariski exact sequence of Andre-Quillen homology. In particular, the relation type,is an invariant of an affine algebraic variety. Also as a consequence of the invariance, we show that in order to calculate the relation type of an ideal in a polynomial ring one can reduce the problem to trinomial ideals. When the relation type is at least two, the extreme equidimensional components play no role. This leads to the non-existence of affine algebras of embedding dimension three and relation type two. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free