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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…
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…
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…