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

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arxiv 2506.14274 v1 pith:UBC7J5I7 submitted 2025-06-17 math.AG math.DS

Zelong Chen , Sheng Meng , Guolei Zhong This is my paper · ORCID
classification math.AGmath.DS
keywords smoothconnectedendomorphismint-amplifiednumberpicardprojectiverationally
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abstract

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 a totally invariant smooth curve of a non-isomorphic surjective endomorphism of $\mathbb{P}^3$ must be a line when it is blowup-equivariant.

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  1. Images of toric variety and amplified endomorphism of weak Fano threefolds

    math.AG 2025-06 conditional novelty 5.0 of 10

    A smooth projective weak Fano threefold of Picard rank 2 that is either a toric image or admits an int-amplified endomorphism is toric, with three explicit non-Fano exceptions.

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