Varieties with many lines
type: Item
instance of: scholarly article
title: Varieties with many lines
zbMATH Open document ID: 0812.14038
DOI: 10.1007/BF02567698
author: Enrico Rogora
published in: Manuscripta Mathematica
publication date: 1995-05-14T00:00:00Z
full work available at URL: https://eudml.org/doc/155928
review text: Let \(X\) be a \(k\)-dimensional irreducible algebraic subvariety of the \(n\)- dimensional complex projective space \(\mathbb{P}^ n\). The author proves that if \(X\) has codimension bigger than two and contains a \((2k - 4)\)- dimensional family of lines, then \(X\) is either a one-dimensional family of quadrics, or a two-dimensional family of \((k-2)\)-dimensional projective spaces, or a linear section of the Grassmann variety of lines of \(\mathbb{P}^ 4\).
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14M07
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 599659
zbMATH Keywords: codimension bigger than two
zbMATH Keywords: Grassmann variety
reviewed by: Eduardo Casas-Alvero
MaRDI profile type: Publication
cites work: Liaison des variétés algébriques. I
cites work: Correspondence
description: scientific article; zbMATH DE number 599659