Quotients of abelian and hyperelliptic surfaces by rational vector fields
type: Item
instance of: scholarly article
title: Quotients of abelian and hyperelliptic surfaces by rational vector fields
zbMATH Open document ID: 0701.14035
DOI: 10.1016/0021-8693(89)90144-0
author: N. E. Zubov
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let S be a non-singular complete algebraic surface defined over an algebraically closed field k of characteristic \(p>0.\) A rational vector field D on S is called a p-closed vector field if there exists a rational function f on S such that \(D^ p=fD\). The quotient surface \(S^ D\) defined by D is normal. Let \(\tilde S^ D\) denote the minimal desingularization of \(S^ D\). The authors investigate the case where S is an abelian surface of a hyperelliptic surface. The conclusion is as follows: (1) \((D)\equiv 0\) (numerical equivalence) \(\Leftrightarrow \kappa (\tilde S^ D)=0\Leftrightarrow \tilde S^ D\) is an abelian surface or a hyperelliptic surface according to the type of S. (2) D has only divisorial singularities and \((D)\not\equiv 0\Leftrightarrow \kappa (\tilde S^ D)=1.\) (3) D has non-divisorial singularities \(\Leftrightarrow \kappa (\tilde S^ D)=2\).
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14K99
zbMATH DE Number: 4148284
zbMATH Keywords: Kodaira dimension
zbMATH Keywords: characteristic p
zbMATH Keywords: rational vector field
zbMATH Keywords: quotient surface
zbMATH Keywords: abelian surface
zbMATH Keywords: hyperelliptic surface
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90144-0
OpenAlex ID: W2083723402
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description: scientific article; zbMATH DE number 4148284