Sheng Meng

activity

20142026

most citedJordan property for non-linear algebraic groups and projective varieties

53 citations · 154 across the 22 of their papers we have counts for

collaborators

24 papers

math.AG2026

Totally invariant subvarieties of $P^{n}$

Yujie Luo, Sheng Meng

Let $f : P_{C}^{n} \to P_{C}^{n}$ be an endomorphism of degree greater than one. We prove that every irreducible Zariski closed subset $V$ with $f^{-1}(V)=V…

math.AG2026

Log Calabi--Yau structure for endomorphisms on $P^{n}$

Yujie Luo, Sheng Meng

Let $f : P^{n} \to P^{n}$ be a $q$ -polarized endomorphism, where $q > 1$ , and let $R_{f}$ be its ramification divisor. We study the singularities of the ramification pair $(\…

math.AG2025

Dynamical Iitaka theory on Fano contractions

Sheng Meng, Long Wang, Tianle Yang

We give several structure theorems for certain surjective endomorphisms on Mori fibre spaces, based on the dynamical Iitaka fibration of the ramification divisor. As an application…

math.AG2025

Jordan property for automorphism groups of compact varieties

Yujie Luo, Sheng Meng, De-Qi Zhang

In this note, we report some recent progress on the Jordan property for (birational) automorphism groups of projective varieties and compact complex varieties.

math.AG2023★ 1 cited

Advances in the equivariant minimal model program and their applications in complex and arithmetic dynamics

Sheng Meng, De-Qi Zhang

This note reports some advances in the Equivariant Minimal Model Program (EMMP) for non-isomorphic surjective endomorphisms and their applications in complex and arithmetic dynamic…

math.AG2023★ 1 cited

Structures theorems and applications of non-isomorphic surjective endomorphisms of smooth projective threefolds

Sheng Meng, De-Qi Zhang

Let $f : X \to X$ be a non-isomorphic (i.e., $deg f > 1$ ) surjective endomorphism of a smooth projective threefold $X$ . We prove that any birational minimal model program become…

math.AG2022★ 2 cited

Moishezon manifolds with no nef and big classes

Jia Jia, Sheng Meng

We show that a compact complex manifold $X$ has no non-trivial nef $(1, 1)$ -classes if there is a non-isomorphic bimeromorphic map $f : X ⇢ Y$ isomorphic in codimen…

math.AG2022

Log Calabi-Yau structure of projective threefolds admitting polarized endomorphisms

Sheng Meng

Let $X$ be a normal projective variety admitting a polarized endomorphism $f$ , i.e., $f^{*} H \sim q H$ for some ample divisor $H$ and integer $q > 1$ . It was conjectured by Broustet and…

math.AG2022★ 2 cited

Equivariant Kähler model for Fujiki's class

Jia Jia, Sheng Meng

Let $X$ be a compact complex manifold in Fujiki's class $C$ , i.e., admitting a big $(1, 1)$ -class $[α]$ . Consider $Aut (X)$ the group of biholomorphic automorphisms…

math.AG2020★ 14 cited

Jordan property for automorphism groups of compact spaces in Fujiki's class $C$

Sheng Meng, Fabio Perroni, De-Qi Zhang

Let $X$ be a compact complex space in Fujiki's Class $C$ . We show that the group $A u t (X)$ of all biholomorphic automorphisms of $X$ has the Jordan property: there is a (Jordan) con…

math.AG2020★ 5 cited

Non-isomorphic endomorphisms of Fano threefolds

Sheng Meng, De-Qi Zhang, Guolei Zhong

Let $X$ be a smooth Fano threefold. We show that $X$ admits a non-isomorphic surjective endomorphism if and only if $X$ is either a toric variety or a product of $P^{1}$ and…

math.AG2020★ 8 cited

Invariant subvarieties with small dynamical degree

Yohsuke Matsuzawa, Sheng Meng, Takahiro Shibata +2

Let $f : X \to X$ be a dominant self-morphism of an algebraic variety over an algebraically closed field of characteristic zero. We consider the set $Σ_{f^{\infty}}$ of $f$ -periodic…

math.AG2020★ 7 cited

Rigidity of rationally connected smooth projective varieties from dynamical viewpoints

Sheng Meng, Guolei Zhong

Let $X$ be a rationally connected smooth projective variety of dimension $n$ . We show that $X$ is a toric variety if and only if $X$ admits an int-amplified endomorphism with total…

math.AG2020★ 10 cited

Non-density of points of small arithmetic degrees

Yohsuke Matsuzawa, Sheng Meng, Takahiro Shibata +1

Given a surjective endomorphism $f : X \to X$ on a projective variety over a number field, one can define the arithmetic degree $α_{f} (x)$ of $f$ at a point $x$ in $X$ . The Kawaguchi…

math.AG2019

Kawaguchi-Silverman conjecture for certain surjective endomorphisms

Sheng Meng, De-Qi Zhang

We prove the Kawaguchi-Silverman conjecture (KSC), about the equality of arithmetic degree and dynamical degree, for every surjective endomorphism of any (possibly singular) projec…

math.AG2019

On endomorphisms of projective varieties with numerically trivial canonical divisors

Sheng Meng

Let $X$ be a klt projective variety with numerically trivial canonical divisor. A surjective endomorphism $f : X \to X$ is amplified (resp.~quasi-amplified) if $f^{*} D - D$ is ample (resp…

math.AG2018★ 1 cited

Normal projective varieties admitting polarized or int-amplified endomorphisms

Sheng Meng, De-Qi Zhang

Let $X$ be a normal projective variety admitting a polarized or int-amplified endomorphism $f$ . We list up characteristic properties of such an endomorphism and classify such a var…

math.AG2018★ 11 cited

Semi-group structure of all endomorphisms of a projective variety admitting a polarized endomorphism

Sheng Meng, De-Qi Zhang

Let $X$ be a projective variety admitting a polarized (or more generally, int-amplified) endomorphism. We show: there are only finitely many contractible extremal rays; and when $X…

math.AG2017

Building blocks of amplified endomorphisms of normal projective varieties

Sheng Meng

Let $X$ be a normal projective variety. A surjective endomorphism $f : X \to X$ is int-amplified if $f^{*} L - L = H$ for some ample Cartier divisors $L$ and $H$ . This is a generaliza…

math.AG2017★ 29 cited

Polarized endomorphisms of normal projective threefolds in arbitrary characteristic

Paolo Cascini, Sheng Meng, De-Qi Zhang

Let $X$ be a projective variety over an algebraically closed field $k$ of arbitrary characteristic $p \geq 0$ . A surjective endomorphism $f$ of $X$ is $q$ -polarized if $f^\ast H \si…

math.AG2017

Characterizations of Toric Varieties via Polarized Endomorphisms

Sheng Meng, De-Qi Zhang

Let $X$ be a normal projective variety and $f : X \to X$ a non-isomorphic polarized endomorphism. We give two characterizations for $X$ to be a toric variety. First we show that if $X…

math.AG2016★ 3 cited

Building blocks of polarized endomorphisms of normal projective varieties

Sheng Meng, De-Qi Zhang

An endomorphism $f$ of a projective variety X is polarized (resp. quasi-polarized) if $f^{*} H$ is linearly equivalent to $q H$ for some ample (resp. nef and big) Cartier divisor $H$ a…

math.AG2015★ 53 cited

Jordan property for non-linear algebraic groups and projective varieties

Sheng Meng, De-Qi Zhang

A century ago, Camille Jordan proved that the complex general linear group $G L_{n} (C)$ has the Jordan property: there is a Jordan constant $C_{n}$ such that every finite subgroup $H \l…

math.AG2014★ 7 cited

Ampleness of canonical divisors of hyperbolic normal projective varieties

Fei Hu, Sheng Meng, De-Qi Zhang

Let X be a projective variety which is algebraic Lang hyperbolic. We show that Lang's conjecture holds (one direction only): X and all its subvarieties are of general type and the…

Totally invariant subvarieties of Pn

Log Calabi--Yau structure for endomorphisms on Pn

Dynamical Iitaka theory on Fano contractions

Jordan property for automorphism groups of compact varieties

Advances in the equivariant minimal model program and their applications in complex and arithmetic dynamics

Structures theorems and applications of non-isomorphic surjective endomorphisms of smooth projective threefolds

Moishezon manifolds with no nef and big classes

Log Calabi-Yau structure of projective threefolds admitting polarized endomorphisms

Equivariant Kähler model for Fujiki's class

Jordan property for automorphism groups of compact spaces in Fujiki's class C

Non-isomorphic endomorphisms of Fano threefolds

Invariant subvarieties with small dynamical degree

Rigidity of rationally connected smooth projective varieties from dynamical viewpoints

Non-density of points of small arithmetic degrees

Kawaguchi-Silverman conjecture for certain surjective endomorphisms

On endomorphisms of projective varieties with numerically trivial canonical divisors

Normal projective varieties admitting polarized or int-amplified endomorphisms

Semi-group structure of all endomorphisms of a projective variety admitting a polarized endomorphism

Building blocks of amplified endomorphisms of normal projective varieties

Polarized endomorphisms of normal projective threefolds in arbitrary characteristic

Characterizations of Toric Varieties via Polarized Endomorphisms

Building blocks of polarized endomorphisms of normal projective varieties

Jordan property for non-linear algebraic groups and projective varieties

Ampleness of canonical divisors of hyperbolic normal projective varieties

Totally invariant subvarieties of $P^{n}$

Log Calabi--Yau structure for endomorphisms on $P^{n}$

Jordan property for automorphism groups of compact spaces in Fujiki's class $C$