Decomposition problem on endomorphisms of projective varieties
type: Item
instance of: scholarly article
title: Decomposition problem on endomorphisms of projective varieties
zbMATH Open document ID: 1069.14010
author: Yoshio Fujimoto
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2004-11-05T00:00:00Z
review text: Let \(X, Y\) be non singular projective varieties \((\dim(Y) = 2,3)\), with \(K_X\) nef and \(K_Y\) not nef, let \(Z = X\times Y\) and \(q : Z \to Y\) be the projection. Suppose that there exists an endomorphism \(f: Z\to Z\) which is not an isomorphism. The author proves that, under suitable conditions concerning the extremal rays of \(Y\), for some integer \(k > 0\), \(f^k\) induces an automorphism \(g : Y\to Y\) such that \(q\circ f^k =g\circ q\).
Mathematics Subject Classification ID: 14D06
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14J15
zbMATH DE Number: 2114253
reviewed by: Luciana Picco Botta
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1145475809
OpenAlex ID: W2065255526
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DOI: 10.2977/PRIMS/1145475809
description: scientific article; zbMATH DE number 2114253