A class of non-algebraic threefolds
type: Item
instance of: scholarly article
title: A class of non-algebraic threefolds
zbMATH Open document ID: 0659.32024
author: Matei Toma
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74828
review text: A holomorphic vector bundle E of rank r on a complex manifold X is called irreducible if it has no coherent subsheaf F of rank r', with \(0<r'<r.\) This notion which is specific to non-algebraic manifolds was brought forward by G. Elencwajg and O. Forster and further studied by C. Banica and J. Le Potier in connection with the problem of existence of holomorphic structures on a given topological vector bundle. In this paper a holomorphic vector bundle is called strongly irreducible if it remains irreducible after any base-change X'\(\to X\). For X a compact surface without curves and \(r=2\), this happens exactly when the threefold \({\mathbb{P}}(E)\) has no divisors. The existence of strongly irreducible bundles on some classes of compact surfaces is proved.
Mathematics Subject Classification ID: 32J15
Mathematics Subject Classification ID: 32L99
zbMATH DE Number: 4077707
zbMATH Keywords: compact complex surface
zbMATH Keywords: non-algebraic surface
zbMATH Keywords: complex threefold
zbMATH Keywords: holomorphic vector bundle
zbMATH Keywords: strongly irreducible bundles
MaRDI profile type: Publication
OpenAlex ID: W2048082089
cites work: Sur l'existence des fibrés vectoriels holomorphes sur les surfaces non-algébriques.
cites work: Q5749404
cites work: Vector bundles on manifolds without divisors and a theorem on deformations
cites work: Complex analytic geometry
cites work: Q3322387
cites work: Q5628266
DOI: 10.5802/AIF.1166
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4077707