Automorphism groups of generic rational surfaces
type: Item
instance of: scholarly article
title: Automorphism groups of generic rational surfaces
zbMATH Open document ID: 0663.14033
DOI: 10.1016/0021-8693(88)90196-2
author: Masanori Koitabashi
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: Let k be an algebraically closed field of arbitrary characteristic. A generic rational surface \(V_ r\) of rank \(r+1\) is the blow up of \({\mathbb{P}}^ 2_ k\) at r points in ``general position'' according to a definition related to that of ``non-special position'' in the sense of \textit{M. Nagata} [Am. J. Math. 81, 766-772 (1959; Zbl 0192.138)]. The author describes the biregular automorphism group \(Aut_ k(V_ r)\) of \(V_ r\) (which actually depends only on r, and not on the choosen points), so providing a unitary proof of many scattered results.
reviewed by: Cristina Turrini
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14J27
Mathematics Subject Classification ID: 14M20
zbMATH DE Number: 4083818
zbMATH Keywords: points in general position
zbMATH Keywords: generic rational surface
zbMATH Keywords: biregular automorphism group
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90196-2
OpenAlex ID: W1965032118
cites work: Q3701635
cites work: Q5580319
cites work: Courbes elliptiques: Formulaire
cites work: Q3887589
cites work: Q5625443
cites work: Q3043288
cites work: RATIONALG-SURFACES
cites work: Blowings-up of \({\mathbb{P}}^ 2\) and their blowings-down
cites work: Q4143433
cites work: Q4402061
cites work: On the automorphisms of hypersurfaces
cites work: Q4163666
cites work: On rational surfaces I. Irreducible curves of arithmetic genus $0$ or $1$
cites work: On rational surfaces, II
cites work: On the 14-th Problem of Hilbert
description: scientific article; zbMATH DE number 4083818