Reconstructing a special double covering of \({\mathbb{P}}^ 3\) from a family of straight lines on it
type: Item
instance of: scholarly article
title: Reconstructing a special double covering of \({\mathbb{P}}^ 3\) from a family of straight lines on it
zbMATH Open document ID: 0722.14003
author: D. Yu. Radionov
published in: Moscow University Mathematics Bulletin
publication date: 1990-01-01T00:00:00Z
review text: Consider a double covering Y of \({\mathbb{P}}^ 3\) branched at a quartic A containing no straight lines. If A is a smooth family of straight lines on the covering Y is parametrized by a surface. \textit{A. S. Tikhomirov} proved that A and consequently Y are recovered from that surface [Math. USSR, Izv. 16, 373-397 (1981); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 44, 415-442 (1980; Zbl 0434.14023)]. In this paper the same is shown for the desingularization X of Y when A has a single double point, after giving a suitable definition of straight lines on X.
reviewed by: Marino Palleschi
Mathematics Subject Classification ID: 14E20
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14E22
zbMATH DE Number: 4189877
zbMATH Keywords: desingularization of covering of projective 3-space
zbMATH Keywords: branching of covering
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4189877