The relation type of affine algebras and algebraic varieties

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Title:	The relation type of affine algebras and algebraic varieties
Author:	Planas Vilanova, Francesc d'Assís
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
Abstract:	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.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Relation type -Rees algebra -Andre-Quillen homology -rees-algebras -ideals -equations -powers -rings -Anells commutatius -Classificació AMS::13 Commutative rings and algebras -Classificació AMS::14 Algebraic geometry::14A Foundations
Rights:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Submitted version Article
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