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

Guolei Zhong

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

Guolei Zhong

Algebraic Geometry · Submitted 29 Sep 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that, if such $X$ admits an int-amplified endomorphism, then $X$ is a $Q$-complex torus.

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arXiv ID2309.17047 (version 1)

Pith IDFHG7T67J, Pith's permanent record of this paper and its review

CitationGuolei Zhong. "Characterization of $Q$-complex tori via endomorphisms -- an addendum to "Int-amplified endomorphisms of compact K\"ahler spaces''." arXiv:2309.17047 (2023). https://pith.science/paper/FHG7T67J

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,088 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.10 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

In this short note, we consider a normal compact K\"ahler klt space $X$ whose canonical divisor $K_X$ is pseudo-effective, and give a dynamical criterion for $X$ to be a $Q$-complex torus. We show that, if such $X$ admits an int-amplified endomorphism, then $X$ is a $Q$-complex torus. As an application, we prove that, if a simply connected compact K\"ahler (smooth) threefold admits an int-amplified endomorphism, then it is (projective and) rationally connected.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this short note, we consider a normal compact K\"ahler klt space $X$ whose canonical divisor $K_X$ is pseudo-effective, and give a dynamical criterion for $X$ to be a $Q$-complex torus.	contribution 0.91	0.87	0.10	asserted 0.87
s1	We show that, if such $X$ admits an int-amplified endomorphism, then $X$ is a $Q$-complex torus.	result 0.99	0.93	0.84	asserted 1.00
s2	As an application, we prove that, if a simply connected compact K\"ahler (smooth) threefold admits an int-amplified endomorphism, then it is (projective and) rationally connected.	result 0.96	0.94	0.13	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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arXiv listing abstract v1

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

In this short note, we consider a normal compact K\"ahler klt space $X$ whose canonical divisor $K_X$ is pseudo-effective, and give a dynamical criterion for $X$ to be a $Q$-complex torus. We show that, if such $X$ admits an int-amplified endomorphism, then $X$ is a $Q$-complex torus. As an application, we prove that, if a simply connected compact K\"ahler (smooth) threefold admits an int-amplified endomorphism, then it is (projective and) rationally connected.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 8 sentences without a confident label

Uses the method or tool of 1 paper

To prove Theorem [ref], we resort to [ref] by showing that $c_1(X)=0∈^2(X,ℝ)$ and $c_2(X)·[ω]^n-2=0$ for some Kähler class $[ω]∈^2(X,ℝ)$.

Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs · Characterization of Q-complex tori · 0.87

Cites as background 1 paper

We say that a compact Kähler space $X$ is a $Q$-complex torus, if there is a finite morphism $T→X$ from a complex torus $T$, which is étale in codimension one (cf. [ref] , [ref] and [ref] ).

Polarized endomorphisms of complex normal varieties · Introduction · 0.98

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