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THE STRUCTURE OF THE TANGENT CONE: AN INTERESTING BIJECTION#.
- Source :
-
Communications in Algebra . Apr2005, Vol. 33 Issue 4, p1043-1052. 10p. - Publication Year :
- 2005
-
Abstract
- Let X = Spec ( R ) be a reduced equidimensional algebraic variety over an algebraically closed field k . Let Y = Spec ( R /??) be a codimension one ordinary multiple subvariety, where ?? is a prime ideal of height 1 of R . If U is a nonempty open subset of Y and ?? a closed point of U , we denote by A ? R ?? its local ring in X , by ?? the extension of ?? in A , and by K the algebraic closure of the residue field k (??). Then there exists a bijection ? ?? : Proj ( G ?? ( A ) ? A /?? k ) ? Proj ( G ( A ?? ) ? k (?? ) K ) such that for every subset S of Proj ( G ?? ( A ) ? A /?? k ), the Hilbert function of S coincides with the Hilbert function of ? ?? (S). We examine some applications. We study the structure of the tangent cone at a closed point of a codimension one ordinary multiple subvariety. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00927872
- Volume :
- 33
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Communications in Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 17000383
- Full Text :
- https://doi.org/10.1081/AGB-200053807