Guolei Zhong

activity

20192026

most citedInvariant subvarieties with small dynamical degree

8 citations · 42 across the 21 of their papers we have counts for

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20 papers · 1 filter

math.AG2026

Positivity of compact Kähler varieties admitting an int-amplified endomorphism

Shin-ichi Matsumura, Guolei Zhong

We study compact Kähler varieties admitting int-amplified endomorphisms from the viewpoint of positivity of tangent sheaves. Our main result shows that the tangent sheaf of such a…

math.AG2026

A note on compact Kähler varieties with pseudo-effective tangent sheaf

Shin-ichi Matsumura, Guolei Zhong

In this paper, we discuss recent developments and open problems concerning the geometry of compact Kähler varieties whose tangent sheaves are pseudo-effective in a strong sense. As…

math.AG2026

Holomorphic symplectic geometry of elliptic surfaces

Jun-Muk Hwang, Guolei Zhong

When a complex surface $X$ admits a nowhere vanishing holomorphic 2-form, it determines a (holomorphic) symplectic structure on $X$ . We study the symplectic geometry of such a symp…

math.AG2025

On smooth rationally connected projective threefolds of Picard number two admitting int-amplified endomorphisms

Zelong Chen, Sheng Meng, Guolei Zhong

We prove that a smooth rationally connected projective threefold of Picard number two is toric if and only if it admits an int-amplified endomorphism. As a corollary, we show that…

math.AG2024★ 1 cited

Kawaguchi-Silverman conjecture for int-amplified endomorphism

Sheng Meng, Guolei Zhong

Let $X$ be a $Q$ -factorial klt projective variety admitting an int-amplified endomorphism $f$ , i.e., the modulus of any eigenvalue of $f^{*} ∣_{NS (X)}$ is greater than…

math.AG2023

Bigness of tangent bundles and dynamical rigidity of Fano manifolds of Picard number 1 (with an appendix by Jie Liu)

Feng Shao, Guolei Zhong

Let $f : X \to Y$ be a surjective morphism of Fano manifolds of Picard number 1 whose VMRTs at a general point are not dual defective. Suppose that the tangent bundle $T_{X}$ is b…

math.AG2023

Characterization of $Q$ -complex tori via endomorphisms -- an addendum to "Int-amplified endomorphisms of compact Kähler spaces''

Guolei Zhong

In this short note, we consider a normal compact Kähler klt space $X$ whose canonical divisor $K_{X}$ is pseudo-effective, and give a dynamical criterion for $X$ to be a $Q$ -complex…

math.AG2023

Positivity of tangent sheaves of projective varieties -- the structure of MRC fibrations

Masataka Iwai, Shin-ichi Matsumura, Guolei Zhong

In this paper, we extend the structure theorem for smooth projective varieties with nef tangent bundle to projective klt varieties whose tangent sheaf is either positively curved o…

math.AG2023★ 1 cited

Smooth projective surfaces with pseudo-effective tangent bundles

Jia Jia, Yongnam Lee, Guolei Zhong

Let $S$ be a non-uniruled (i.e., non-birationally ruled) smooth projective surface. We show that the tangent bundle $T_{S}$ is pseudo-effective if and only if the canonical divisor $…

math.AG2022★ 2 cited

Boundedness of finite morphisms onto Fano manifolds with large Fano index

Feng Shao, Guolei Zhong

Let $f : Y \to X$ be a finite morphism between Fano manifolds $Y$ and $X$ such that the Fano index of $X$ is greater than 1. On the one hand, when both $X$ and $Y$ are fourfolds of Pi…

math.AG2022★ 1 cited

Existence of the equivariant minimal model program for compact Kähler threefolds with the action of an abelian group of maximal rank

Guolei Zhong

Let $X$ be a $Q$ -factorial compact Kähler klt threefold admitting an action of a free abelian group $G$ , which is of positive entropy and of maximal rank. After running th…

math.AG2021★ 2 cited

Strictly nef divisors on singular threefolds

Juanyong Wang, Guolei Zhong

Let $X$ be a normal projective variety with only klt singularities, and $L_{X}$ a strictly nef $Q$ -divisor on $X$ . In this paper, we study the singular version of Serrano's…

math.AG2021★ 5 cited

Algebraic fibre spaces with strictly nef relative anti-log canonical divisor

Jie Liu, Wenhao Ou, Juanyong Wang +2

Let $(X, Δ)$ be a projective klt pair, and $f : X \to Y$ a fibration to a smooth projective variety $Y$ with strictly nef relative anti-log canonical divisor $- (K_{X / Y} + Δ)$ . We prove t…

math.AG2021

Strictly nef divisors on singular threefolds

Guolei Zhong

Let $X$ be a normal projective threefold with mild singularities, and $L_{X}$ a strictly nef $Q$ -divisor on $X$ . First, we show the ampleness of $K_{X} + t L_{X}$ with sufficiently…

math.AG2020★ 4 cited

Amplified endomorphisms of Fano fourfolds

Jia Jia, Guolei Zhong

Let $X$ be a smooth Fano fourfold admitting a conic bundle structure. We show that $X$ is toric if and only if $X$ admits an amplified endomorphism; in this case, $X$ is a rational…

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.AG2019★ 3 cited

Int-amplified endomorphisms of compact Kähler spaces

Guolei Zhong

Let $X$ be a normal compact Kähler space of dimension $n$ . A surjective endomorphism $f$ of such $X$ is int-amplified if $f^{*} ξ - ξ = η$ for some Kähler classes $ξ$ and $η$ . First, we s…

math.AG2019★ 2 cited

Totally invariant divisors of int-amplified endomorphisms of normal projective varieties

Guolei Zhong

We consider an arbitrary int-amplified surjective endomorphism $f$ of a normal projective variety $X$ over $C$ and its $f^{- 1}$ -stable prime divisors. We extend the early…

Positivity of compact Kähler varieties admitting an int-amplified endomorphism

A note on compact Kähler varieties with pseudo-effective tangent sheaf

Holomorphic symplectic geometry of elliptic surfaces

On smooth rationally connected projective threefolds of Picard number two admitting int-amplified endomorphisms

Kawaguchi-Silverman conjecture for int-amplified endomorphism

Bigness of tangent bundles and dynamical rigidity of Fano manifolds of Picard number 1 (with an appendix by Jie Liu)

Characterization of Q-complex tori via endomorphisms -- an addendum to "Int-amplified endomorphisms of compact Kähler spaces''

Positivity of tangent sheaves of projective varieties -- the structure of MRC fibrations

Smooth projective surfaces with pseudo-effective tangent bundles

Boundedness of finite morphisms onto Fano manifolds with large Fano index

Existence of the equivariant minimal model program for compact Kähler threefolds with the action of an abelian group of maximal rank

Strictly nef divisors on singular threefolds

Algebraic fibre spaces with strictly nef relative anti-log canonical divisor

Strictly nef divisors on singular threefolds

Amplified endomorphisms of Fano fourfolds

Non-isomorphic endomorphisms of Fano threefolds

Invariant subvarieties with small dynamical degree

Rigidity of rationally connected smooth projective varieties from dynamical viewpoints

Int-amplified endomorphisms of compact Kähler spaces

Totally invariant divisors of int-amplified endomorphisms of normal projective varieties

Characterization of $Q$ -complex tori via endomorphisms -- an addendum to "Int-amplified endomorphisms of compact Kähler spaces''