On branched coverings of quadrics
type: Item
instance of: scholarly article
title: On branched coverings of quadrics
zbMATH Open document ID: 0853.14006
DOI: 10.1007/BF01196169
author: Meeyoung Kim
published in: Archiv der Mathematik
publication date: 1997-01-14T00:00:00Z
review text: Using the ``\(k\)-ampleness'' (in the sense of Sommese) of the vector bundle associated with a branched covering, \(f : X \to {\mathcal Q}_n\), of the smooth quadric \({\mathcal Q}_n\), we prove that \(f\) induces \(\mathbb{C}\)-cohomology isomorphisms between \(X\) and \({\mathcal Q}_n\) in a certain range of cohomology and homotopy dimensions, provided the degree of the covering is small enough.
Mathematics Subject Classification ID: 14E20
Mathematics Subject Classification ID: 14J99
zbMATH DE Number: 938577
zbMATH Keywords: Lefschetz type theorems
zbMATH Keywords: \(k\)-ampleness
zbMATH Keywords: branched covering
zbMATH Keywords: smooth quadric
reviewed by: Myung-Soo Kim
MaRDI profile type: Publication
cites work: Formale Geometrie und homogene Räume
cites work: Ampleness and Connectedness in Complex G/P
cites work: On the ramification of branched coverings of \(\mathbb{P}^n\)
cites work: Q4143433
cites work: A Barth-Lefschetz type theorem for branched coverings of Grassmannians.
cites work: Lectures on Curves on an Algebraic Surface. (AM-59)
cites work: Submanifolds of Abelian varieties
cites work: Complex subspaces of homogeneous complex manifolds II—Homotopy Results
cites work: Q3661887
Recommended article: Signatures of branched coverings and solvability in quadratures
Recommended article: Q4699485
Recommended article: Q3704180
Recommended article: Triple coverings of the projective plane branched along quintic curves
Recommended article: Q4384012
Recommended article: On branched coverings of projective manifolds
Recommended article: Two results on branched coverings of Grassmannians
Recommended article: Branched coverings over \(\mathbb C^2\) and the Jacobian conjecture
Recommended article: COVERS OF GENERALIZED QUADRANGLES
Recommended article: Quadrics and normal generation of line bundles on multiple coverings
description: scientific article; zbMATH DE number 938577