A note on Sakai's theorem concerning polarized normal surfaces
type: Item
instance of: scholarly article
title: A note on Sakai's theorem concerning polarized normal surfaces
zbMATH Open document ID: 1083.14514
author: Hideo Kojima
published in: Archiv der Mathematik
publication date: 2003-08-18T00:00:00Z
review text: Let \(Y\) be a normal projective surface and \(Y\) an ample Cartier divisor on \(X\). The author generalizes earlier classification results of such polarized normal surfaces in terms of the logarithmic Kodaira dimension to the case of algebraically closed fields of arbitrary characteristic. More precisely, \textit{F. Sakai} [J. Reine Angew. Math. 366, 121--128 (1986; Zbl 0582.14011)] completed this classification in the case of characteristic zero. While most of his arguments are independent of the characteristic, a vanishing theorem used there does not hold if \(\text{char}(k)>0\), and the classification theory of normal surfaces in characteristic zero is used. In the paper under review, the author avoids this problems by using a result of \textit{H. Terakawa} [Pac. J. Math. 187, No.1, 187--199 (1999; Zbl 0967.14008)] and himself [Arch. Math. 77, No.6, 517--521 (2001; Zbl 1063.14046)].
reviewed by: Olaf Teschke
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 14C20
zbMATH DE Number: 1966445
MaRDI profile type: Publication
full work available at URL: s00013-003-4598-z
OpenAlex ID: W121390499
DOI: 10.1007/S00013-003-4598-Z
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description: scientific article; zbMATH DE number 1966445