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2014 The algebraic dynamics of generic endomorphisms of $\mathbb{P}^n$
Najmuddin Fakhruddin
Algebra Number Theory 8(3): 587-608 (2014). DOI: 10.2140/ant.2014.8.587

Abstract

We investigate some general questions in algebraic dynamics in the case of generic endomorphisms of projective spaces over a field of characteristic zero. The main results that we prove are that a generic endomorphism has no nontrivial preperiodic subvarieties, any infinite set of preperiodic points is Zariski-dense and any infinite subset of a single orbit is also Zariski-dense, thereby verifying the dynamical “Manin–Mumford” conjecture of Zhang and the dynamical “Mordell–Lang” conjecture of Denis and Ghioca and Tucker in this case.

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Najmuddin Fakhruddin. "The algebraic dynamics of generic endomorphisms of $\mathbb{P}^n$." Algebra Number Theory 8 (3) 587 - 608, 2014. https://doi.org/10.2140/ant.2014.8.587

Information

Received: 30 November 2012; Revised: 25 May 2013; Accepted: 4 July 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1317.37116
MathSciNet: MR3218803
Digital Object Identifier: 10.2140/ant.2014.8.587

Subjects:
Primary: 37P55
Secondary: 37F10

Keywords: generic endomorphisms , projective space

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.8 • No. 3 • 2014
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