Quelques calculs dans les variétés d'alignements. (Some calculations in line varieties)
type: Item
instance of: scholarly article
title: Quelques calculs dans les variétés d'alignements. (Some calculations in line varieties)
zbMATH Open document ID: 0621.14031
DOI: 10.1016/0001-8708(87)90006-5
author: Patrick Le Barz
published in: Advances in Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The author interpretes the k-secant linear varieties of an algebraic variety X (over an algebraically closed field of characteristic zero) as elements of the Hilbert scheme \(Hilb^ kX\) parametrizing zero- dimensional subschemes of length k and, then he uses intersection theory to obtain formulas for k-secant lines. In particular many classical formulas for curves are verified.
Mathematics Subject Classification ID: 14N10
Mathematics Subject Classification ID: 14C05
zbMATH DE Number: 4006430
zbMATH Keywords: k-secant linear varieties
zbMATH Keywords: Hilbert scheme
reviewed by: Eduardo Casas-Alvero
MaRDI profile type: Publication
full work available at URL: 0001-8708(87)90006-5
OpenAlex ID: W1998079130
cites work: Algebraic Families on an Algebraic Surface
cites work: Q4165449
cites work: Géométrie des schémas de Hilbert ponctuels
cites work: Q4195061
cites work: Un théorème sur les homomorphismes de schemas abeliens
cites work: Q3312364
cites work: Q4143433
cites work: Reducibility of the families of O-dimensional schemes on a variety
cites work: Q4175681
cites work: Platitude et non-platitude de certains sous-schémas de Hilb k PN.
cites work: Q3659909
cites work: The Secant Bundle of a Projective Variety
cites work: Q5801760
cites work: Secant Spaces to Curves
cites work: Q3803245
cites work: La variété des triplets complets. (The variety of complete triplets)
description: scientific article; zbMATH DE number 4006430