Codimension 2 subvarieties of projective space
type: Item
instance of: scholarly article
title: Codimension 2 subvarieties of projective space
zbMATH Open document ID: 0716.14032
DOI: 10.1007/BF01172790
author: Audun Holme
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155450
review text: Hartshorne conjectures that if Y is a smooth projective variety of codimension 2 in \({\mathbb{P}}^ n (n\geq 6)\), then Y is a complete intersection. Let E be a rank 2 bundle on projective n-space and X be a codimension 2 zero-scheme of a section of E. Using a construction of Ran, the author studies the secant variety of X. He concludes that X is a complete intersection under various numerical assumptions on X. He also studies unstable rank 2 bundles and numerically split bundles.
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 14M07
zbMATH DE Number: 4179547
zbMATH Keywords: Hartshorne conjecture
zbMATH Keywords: complete intersection
zbMATH Keywords: secant variety
zbMATH Keywords: split bundles
reviewed by: Lawrence Ein
MaRDI profile type: Publication
cites work: Komplexe Unterräume und holomorphe Vektorraumbündel vom Rang zwei
cites work: Stable vector bundles of rank 2 on \(P^ 3\)
cites work: A computer aided approach to codimension 2 subvarities of Pn, n6.
cites work: On projective varieties of codimension 2
cites work: Nonstable Reflexive Sheaves on P 3
cites work: Q3924327
description: scientific article; zbMATH DE number 4179547