Degeneration of Kunev surfaces. I
type: Item
instance of: scholarly article
title: Degeneration of Kunev surfaces. I
zbMATH Open document ID: 0698.14038
author: Sampei Usui
published in: Proceedings of the Japan Academy. Series A
publication date: 1987-01-01T00:00:00Z
review text: A Kunev surface is a minimal surface X of general type with \(p_ g=c^ 2_ 1=1\) having an involution \(\alpha\) : \(X\to X\) such that \(Y'=X/\alpha\) is a K3 surface with rational double points and the bicanonical map of X is a Galois cover of \({\mathbb{P}}^ 2\) factoring through \(Y'\). In the note under review the author formulates two theorems describing degenerations of Kunev surfaces over a fixed K3 surface. Using these theorems, the author gives a uniform explanation for the failure of the Torelli theorem for the period map \(\Phi_ 2\) of the pure second cohomology of Kunev surfaces and elliptic surfaces with \(p_ g=1\) and \(q=0, 1\). There are no proofs.
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 14D20
zbMATH DE Number: 4144146
zbMATH Keywords: degeneration
zbMATH Keywords: Kunev surface
zbMATH Keywords: \(K3\) surface
zbMATH Keywords: Torelli theorem
reviewed by: F. L. Zak
MaRDI profile type: Publication
full work available at URL: pjaa.63.110
OpenAlex ID: W4235367938
cites work: Q3856874
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DOI: 10.3792/PJAA.63.110
description: scientific article; zbMATH DE number 4144146