On quintic \(K\)-3 surfaces
type: Item
instance of: scholarly article
title: On quintic \(K\)-3 surfaces
zbMATH Open document ID: 0744.14027
published in: Chinese Annals of Mathematics. Series B
publication date: 1992-06-25T00:00:00Z
review text: Irreducible quintic surfaces with one-dimensional singular loci in the three-dimensional projective space are studied in this paper under the condition that they are birationally isomorphic to \(K3\) surfaces. In the first part three kinds of methods to construct such quintic surfaces starting from smooth \(K3\) surfaces are given. In the second part it is shown that conversely quintic surfaces satisfying the conditions can be constructed by one of methods in the first part under certain generic conditions. These generic conditions are not so clear. It is an interesting problem to eliminate these conditions. Besides, it may be interesting to consider further whether a quintic surface with a singular locus along a line and with a double point outside this line can be birationally isomorphic to a \(K3\) surface.
reviewed by: Tohsuke Urabe
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 14J17
zbMATH DE Number: 11937
zbMATH Keywords: quintic surfaces with one-dimensional singular loci
zbMATH Keywords: \(K3\) surfaces
author: Jingen Yang
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 11937