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arXiv · 2606.24103

Essential dimensions of polarized endomorphisms of certain algebraic surfaces

Qianli Fang·Yujie Luo·De-Qi Zhang
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Abstract

Let $f: X \to X$ be a polarized endomorphism of a smooth projective surface which is birationally ruled. We answer a question of Koll\'ar and Zhuang, in the affirmative, on the incompressibility of $f$, under the assumption that $f$ is Galois and an explicit lower bound of deg$(f)$ depending only on $X$. We also give examples showing the optimality of such a lower bound.

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Qianli Fang, Yujie Luo, De-Qi Zhang. 2026-06-23. Essential dimensions of polarized endomorphisms of certain algebraic surfaces. https://arxiv.org/abs/2606.24103

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