The tangent bundle of a ruled surface
type: Item
instance of: scholarly article
title: The tangent bundle of a ruled surface
zbMATH Open document ID: 0541.14035
DOI: 10.1007/BF01456133
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163985
review text: Let Z be a ruled surface. The authors settle, in the case of decomposable Z, the questions of existence and classification of sublinebundles of the tangent bundle \(T_ Z\). They also show, in the indecomposable case, that \(T_ Z\) splits in general in the sense of moduli (if the ground field has characteristic not 2). The ''integrable'' sublinebundles of \(T_ Z\) give rise to ''quotient'' surfaces Y of Z, which exhibit various interesting ''pathological'' features. One obtains, for instance, surfaces Y of general type with global vector fields. These quotient surface examples were worked out in collaboration with H. Kurke; a more detailed analysis of them is forthcoming.
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14J17
zbMATH DE Number: 3859306
zbMATH Keywords: decomposable ruled surface
zbMATH Keywords: sublinebundles of the tangent bundle
zbMATH Keywords: quotient surface
author: Richard Ganong
author: Peter Russell
MaRDI profile type: Publication
cites work: Complex Fibre Bundles and Ruled Surfaces
cites work: Plane Frobenius Sandwiches
cites work: Derivations with only divisorial singularities on rational and ruled surfaces
cites work: Q4724753
cites work: Q4143433
cites work: Q5616640
cites work: Geometric structure of the cohomology rings in abstract algebraic geometry
cites work: On Self-Intersection Number of a Section on a Ruled Surface
cites work: INSEPARABLE MORPHISMS OF ALGEBRAIC SURFACES
cites work: Forms of the affine line and its additive group
description: scientific article; zbMATH DE number 3859306