57 citations · 128 across the 26 of their papers we have counts for
33 papers
Dynamical degrees of twisted rational maps
Marc Abboud, Junyi Xie
Twisted rational maps arise naturally in relative algebraic dynamics: if a rational self-map preserves a fibration, then the induced map on the generic fiber is usually not an ordi…
Recent progress on the geometric Bombieri--Lang conjecture
Junyi Xie
We survey recent progress on the geometric Bombieri--Lang conjecture over function fields of characteristic zero. We discuss recent work of Xie--Yuan and Guoquan Gao, which togethe…
The Geometric Bombieri-Lang Conjecture for Ramified Covers of Abelian Varieties
Junyi Xie, Xinyi Yuan
In this paper, we prove the geometric Bombieri-Lang conjecture for projective varieties which have finite morphisms to abelian varieties of trivial traces over function fields of c…
Space spanned by characteristic exponents
Zhuchao Ji, Junyi Xie, Geng-Rui Zhang
We prove several rigidity results on multiplier spectrum and length spectrum. For example, we show that for every non-exceptional rational map $f:\mathbb{P}^1(\mathbb{C})\to\mathbb…
Around the dynamical Mordell-Lang conjecture
Junyi Xie
There are three aims of this note. The first one is to report some advances around the dynamical Mordell-Lang (=DML) conjecture. Second, we generalize some known results. For examp…
Partial Heights, Entire Curves, and the Geometric Bombieri-Lang Conjecture
Junyi Xie, Xinyi Yuan
We introduce a new approach to the geometric Bombieri--Lang conjecture for hyperbolic varieties in characteristic 0. The main idea is to construct an entire curve on a special fibe…
DAO for curves
Zhuchao Ji, Junyi Xie
We prove the Dynamical André-Oort (DAO) conjecture proposed by Baker and DeMarco for families of rational maps parameterized by an algebraic curve. In fact, we prove a stronger res…
Local rigidity of Julia sets
Zhuchao Ji, Junyi Xie
We find criteria ensuring that a local (holomorphic, real analytic, ) homeomorphism between the Julia sets of two given rational functions comes from an algebraic corresponden…
Topological entropy of a rational map over a complete metrized field
Charles Favre, Tuyen Trung Truong, Junyi Xie
We prove that the topological entropy of any dominant rational self-map of a projective variety defined over a complete non-Archimedean field is bounded from above by the maximum o…
Homoclinic orbits, multiplier spectrum and rigidity theorems in complex dynamics
Zhuchao Ji, Junyi Xie
The aims of this paper are to answer several conjectures and questions about multiplier spectrum of rational maps and to give new proofs of several rigidity theorems in complex dyn…
Algebraicity criteria, invariant subvarities and transcendence problems from arithmetic dynamics
Junyi Xie
We introduce an algebraicity criteria. It has the following form: under certain conditions, an analytic subvariety of some algebriac variety over a global field , if it contains…
Geometric Bogomolov conjecture in arbitrary characteristics
Junyi Xie, Xinyi Yuan
The goal of this paper is to prove the full geometric Bogomolov conjecture. We first reduce it to the case that the extension of the base fields has transcendence degree 1, and the…
Remarks on algebraic dynamics in positive characteristic
Junyi Xie
In this paper, we study arithmetic dynamics in arbitrary characteristic, in particular in positive characteristic. We generalise some basic facts on arithmetic degree and canonical…
Endomorphisms of quasi-projective varieties -- towards Zariski dense orbit and Kawaguchi-Silverman conjectures
Jia Jia, Takahiro Shibata, Junyi Xie +1
Let be a quasi-projective variety and a finite surjective endomorphism. We consider Zariski Dense Orbit Conjecture (ZDO), and Adelic Zariski Dense Orbit Conjec…
Continuous functions on Berkovich spaces
Junyi Xie
Let be a perfect complete valued field with a nontrivial non-archimedean norm and with Let be a reduced and normal -analytic space. Then $O…
Three chapters on Cremona groups
Serge Cantat, Julie Déserti, Junyi Xie
In the first part of this article, we answer a question of I. Dolgachev, which is related to the following problem: given a birational map $f\in\mathrm{Bir}(\mathbb{P}^m_\mathbf{k}…
Birational conjugacies between endomorphisms on the projective plane
Serge Cantat, Junyi Xie
We proved that, in characteristic 0, if two dominant endomorphisms of the projective plane of degree at least 2 are conjugate by some birational transformation, then they are conju…
Surjective endomorphisms of projective surfaces: the existence of infinitely many dense orbits
Jia Jia, Junyi Xie, De-Qi Zhang
Let be a surjective endomorphism of a normal projective surface. When , applying an (iteration of) -equivariant minimal model pro…
Free actions of large groups on complex threefolds
Serge Cantat, Olga Paris-Romaskevich, Junyi Xie
We classify compact Kähler threefolds with a free group of automorphisms acting freely on .
Families of commuting automorphisms, and a characterization of the affine space
Serge Cantat, Andriy Regeta, Junyi Xie
In this paper we show that an affine space is determined by the abstract group structure of its group of regular automorphisms in the category of connected affine varieties. To pro…
Finiteness properties of pseudo-hyperbolic varieties
Ariyan Javanpeykar, Junyi Xie
Motivated by Lang-Vojta's conjecture, we show that the set of dominant rational self-maps of an algebraic variety over a number field with only finitely many rational points in any…
The existence of Zariski dense orbits for endomorphisms of projective surfaces (with an appendix in collaboration with Thomas Tucker)
Junyi Xie
In this paper we prove the following theorem. Let be a dominant endomorphism of a smooth projective surface over an algebraically closed field of characteristic . If there i…
On Fano manifolds of Picard number one with big automorphism groups
Baohua Fu, Wenhao Ou, Junyi Xie
Let be an -dimensional smooth Fano complex variety of Picard number one. Assume that the VMRT at a general point of is smooth irreducible and non-degenerate (which holds…
The geometric Bogomolov conjecture
Serge Cantat, Ziyang Gao, Philipp Habegger +1
We prove the geometric Bogomolov conjecture over a function field of characteristic zero.