The Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane
In this paper we prove the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane.
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arXiv subjects
Junyi Xie
Publications and source records attributed to Junyi Xie.
Intersection of valuation rings in $k[x,y]$
We associate to any given finite set of valuations on the polynomial ring in two variables over an algebraically closed field a numerical invariant whose positivity characterizes the case when the intersection of their valuation rings has maximal transcendence degree over the base fields. As an application, we give a criterion for when an analytic branch at infinity in the affine plane that is defined over a number field in a suitable sense is the branch of an algebraic curve.
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Dynamical Mordell-Lang conjecture for birational polynomial morphisms on $\mathbb{A}^2$
We prove the dynamical Mordell-Lang conjecture for birational polynomial morphisms on $\mathbb{A}^2$.
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Periodic points of birational maps on projective surfaces
We classify birational maps of projective smooth surfaces whose non-critical periodic points are Zariski dense. In particular, we show that if the first dynamical degree is greater than one, then the periodic points are Zariski dense.
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