Junyi Xie

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20182022

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4 papers · 1 filter

math.AG2019

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…

math.AG2018

On Fano manifolds of Picard number one with big automorphism groups

Baohua Fu, Wenhao Ou, Junyi Xie

Let $X$ be an $n$ -dimensional smooth Fano complex variety of Picard number one. Assume that the VMRT at a general point of $X$ is smooth irreducible and non-degenerate (which holds…

math.AG2018

Algebraic dynamics of skew-linear self-maps

Dragos Ghioca, Junyi Xie

Let $X$ be a variety defined over an algebraically closed field $k$ of characteristic $0$ , let $N \in N$ , let $g : X ⇢ X$ be a dominant rational self-map, and let…

math.AG2018

On degrees of birational mappings

Serge Cantat, Junyi Xie

We prove that the degrees of the iterates $deg (f^{n})$ of a birational map satisfy $lim inf (deg (f^{n})) < + \infty$ if and only if the sequence $deg (f^{n})$ is bounded, an…