Questions on self maps of algebraic varieties

Abstract

In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.

Cited by in corpus (57)

• Periodic points of birational maps on projective surfaces
• Remarks on endomorphisms and rational points
• Polarized endomorphisms of uniruled varieties (with Appendix by Y. Fujimoto and N. Nakayama)
• The existence of Zariski dense orbits for polynomial endomorphisms of the affine plane
• Growth of the number of periodic points for meromorphic maps
• Equidistribution of Dynamically Small Subvarieties over the Function Field of a Curve
• The arithmetic Hodge index theorem for adelic line bundles II
• The Geometric Dynamical Northcott and Bogomolov Properties
• Semi-group structure of all endomorphisms of a projective variety admitting a polarized endomorphism
• Non-density of points of small arithmetic degrees
• The existence of Zariski dense orbits for endomorphisms of projective surfaces (with an appendix in collaboration with Thomas Tucker)
• Invariant subvarieties with small dynamical degree
• Rigidity of rationally connected smooth projective varieties from dynamical viewpoints
• The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for split rational maps
• Int-amplified endomorphisms on normal projective surfaces
• Relative Clifford inequality for varieties fibered by curves
• Uniform boundedness of rational points and preperiodic points
• Théorèmes d'équidistribution pour les systèmes dynamiques d'origine arithmétique
• Amplified endomorphisms of Fano fourfolds
• Isotriviality is equivalent to potential good reduction for endomorphisms of ${\mathbb{P}}^N$ over function fields
• Int-amplified endomorphisms of compact Kähler spaces
• Uniform bounds for pre-periodic points in families of twists
• Heights and arithmetic dynamics over finitely generated fields
• The (non-uniform) Hrushovski-Lang-Weil estimates
• Building blocks of polarized endomorphisms of normal projective varieties
• Invariant hypersurfaces of endomorphisms of projective varieties
• Zero Order Estimates for Analytic Functions
• Preperiodic points of polynomials over global fields
• The equidistribution of small point for strongly regular pairs of polynomial maps
• Boundedness of finite morphisms onto Fano manifolds with large Fano index
• Totally invariant divisors of int-amplified endomorphisms of normal projective varieties
• A Tits alternative for rational functions
• Periods of rational maps modulo primes
• Almost Newton, sometimes Lattès
• Endomorphisms of projective varieties
• Normal projective varieties admitting polarized or int-amplified endomorphisms
• A Uniform Field-of-Definition/Field-of-Moduli Bound for Dynamical Systems on ${\mathbf{P}}^N$
• Fixed points of smooth varieties with Kodaira dimension zero
• Codimension one attracting sets in ${\mathbb{P}}^k(\mathbb{C})$
• Periodic points, linearizing maps, and the dynamical Mordell-Lang problem
• Rational preimages in families of dynamical systems
• Polarized endomorphisms of complex normal varieties
• The Hrushovski-Lang-Weil estimates
• Hyperbolic polarized dynamics, pairs of inverse maps and the Dirichlet property
• Potential density of projective varieties having an int-amplified endomorphism
• Lifting finite self maps of equicharacteristic complete local rings
• Isotriviality and the space of morphisms on projective varieties
• Hauteurs canoniques des sous-variétés toriques
• The $abcd$ conjecture, uniform boundedness, and dynamical systems
• On endomorphisms of projective varieties with numerically trivial canonical divisors
• Quadratic rational functions with a rational periodic critical point of period 3
• Finding Rational Periodic Points on Wehler K3 Surfaces
• Endomorphisms of hypersurfaces of Fano manifolds of Picard number 1
• Some applications of p-adic uniformization to algebraic dynamics
• Variation of the canonical height in a family of polarized dynamical systems
• Finiteness of commutable maps of bounded degree
• A Gap Principle for Subvarieties with Finitely Many Periodic Points