Unirationality of Ueno-Campana's threefold
type: Item
instance of: scholarly article
title: Unirationality of Ueno-Campana's threefold
zbMATH Open document ID: 1304.14064
author: Keiji Oguiso
author: Tuyen Trung Truong
author: Fabrizio Catanese
published in: Manuscripta Mathematica
publication date: 2014-11-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1310.3569
review text: The paper under review proves that a threefold constructed by \textit{K. Ueno} [Classification theory of algebraic varieties and compact complex spaces. Notes written in collaboration with P. Cherenack. York: Springer-Verlag (1975; Zbl 0299.14007)] and revisited by \textit{F. Campana} [in: Classification of algebraic varieties. Based on the conference on classification of varieties, Schiermonnikoog, Netherlands, May 2009. Zürich: European Mathematical Society (EMS). 115--121 (2011; Zbl 1219.14063)] is unirational, thus answering a question of Campana and Ueno. The proof is by explicitly writing down an equation for the affine part and noticing that this is a conic bundle with a multisection which is a rational surface. Note that Colliot-Thélène has proved that the same example is rational [``Rationalité d'un fibré en coniques'', preprint, \url{arxiv 1310.5402}].
reviewed by: Zhiyu Tian
Mathematics Subject Classification ID: 14M20
Mathematics Subject Classification ID: 14E08
zbMATH DE Number: 6369213
zbMATH Keywords: unirational
MaRDI profile type: Publication
OpenAlex ID: W2057081423
arXiv ID: 1310.3569
cites work: Q2997046
cites work: Rationality of a tapered fiber
cites work: Explicit examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy
cites work: Classification theory of algebraic varieties and compact complex spaces. Notes written in collaboration with P. Cherenack
DOI: 10.1007/S00229-014-0680-Z
Recommended article: A remark on the Ueno-Campana's threefold
Recommended article: The Universal Kummer Threefold
Recommended article: Логика, единство в трёх лицах
Recommended article: The unity of a Tractarian fact
Recommended article: Frege’s Unification
Recommended article: On the logic of unification
Recommended article: Structuralism, Invariance, and Univalence
Recommended article: Q5040167
Recommended article: Q5461159
Recommended article: Q3558396
description: scientific article; zbMATH DE number 6369213