Gaussian maps for double coverings
type: Item
instance of: scholarly article
title: Gaussian maps for double coverings
zbMATH Open document ID: 0805.14005
DOI: 10.1007/BF02567687
author: Jeanne Duflot
published in: Manuscripta Mathematica
publication date: 1995-02-05T00:00:00Z
full work available at URL: https://eudml.org/doc/155917
review text: Given a line bundle \(L\) on a smooth projective variety \(X\), the Gauss map \[ \bigwedge^ 2 H^ 0(X,L) \to H^ 0 (X,L^{\otimes 2}) \] is defined by sending \(\sum s_ i \otimes t_ i\) to \(\sum(ds_ i\otimes t_ i- s_ i\otimes dt_ i)\). If \(X \to Y\) is a cyclic covering, with \(Y\) and \(X\) smooth and projective, and \(L\) is a pull-back from \(Y\), then, using projection formulas, it is possible to express the Gauss map for \(L\) in terms of similar maps on \(Y\). After having described this general setting, the author focuses on the case of double covers of \(\mathbb{P}^ m\) \((m>1)\) and computes the cokernel of the Gauss map for the pull-back of any effective line bundle on \(\mathbb{P}^ m\). The paper also contains several references on the general theory and applications of the Gauss maps.
Mathematics Subject Classification ID: 14E20
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 554378
zbMATH Keywords: projection
zbMATH Keywords: Gauss map
zbMATH Keywords: double covers
reviewed by: Rita Pardini
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 554378