Rank two vector bundles on \({\mathbb P}^ n\) uniform with respect to some rational curves
type: Item
instance of: scholarly article
title: Rank two vector bundles on \({\mathbb P}^ n\) uniform with respect to some rational curves
zbMATH Open document ID: 0637.14011
DOI: 10.1007/BF01207481
author: Mirella Manaresi
author: Monica Idà
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: A classical method for studying the classifying vector bundles on projective spaces is to study their restrictions to linear subvarieties. For example, it is well known that a vector bundle on \({\mathbb{P}}^ n \) of rank \(r\leq n,\) whose restriction to all lines has the same splitting type is homogeneous. Let E be a rank two vector bundle on \({\mathbb{P}}^ n,\) whose restriction to all rational smooth curves of degree \(d\) in \({\mathbb{P}}^ n \)has constant splitting type. In this paper we prove that if \(d=2\), or \(d=3\) and \(c_ 1(E)\) is even, then E is homogeneous.
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 4037986
zbMATH Keywords: rank two vector bundle
zbMATH Keywords: splitting type
MaRDI profile type: Publication
cites work: Des fibres uniformes non homogènes
cites work: Stable rank-2 vector bundles on \(\mathbb{P}_2\) with \(c_1\) odd
cites work: Vector bundles on complex projective spaces
description: scientific article; zbMATH DE number 4037986