Sections hyperplanes des surfaces K3
type: Item
instance of: scholarly article
title: Sections hyperplanes des surfaces K3
zbMATH Open document ID: 0663.14028
DOI: 10.1215/S0012-7094-87-05541-4
author: Arnaud Beauville
author: J.-Y. Mérindol
published in: Duke Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: \textit{J. M. Wahl} [Duke Math. J. 55, 843-871 (1987; Zbl 0644.14001)] proved that if C is a smooth hyperplane section of a K3 surface then the natural map \(\phi_ K:\quad \bigwedge^ 2H^ 0(C,\quad \omega_ C)\to H^ 0\quad (C,\omega_ C^{\otimes^ 3}),\) given essentially by \(s\wedge t\mapsto sdt-tds,\) is not surjective. The authors prove that if C is a hyperplane section of a K3 surface S then the surjectivity of \(\phi_ K\) implies that the exact sequence \[ 0\quad \to \quad T_ C\quad \to \quad T_{S| C}\quad \to \quad N_{C/S}\quad \to \quad 0 \] splits, which in turn implies the existence of an involution of S with fixed locus equal to C. The result of Wahl is then easily deduced.
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 14C17
zbMATH DE Number: 4083813
zbMATH Keywords: hyperplane section of a K3 surface
reviewed by: Balwant Singh
MaRDI profile type: Publication
cites work: Q4143433
cites work: Varieties Defined by Quadratic Equations
cites work: Projective Models of K - 3 Surfaces
cites work: The Jacobian algebra of a graded Gorenstein singularity
description: scientific article; zbMATH DE number 4083813