Kawaguchi-Silverman conjecture for int-amplified endomorphism

Sheng Meng; Guolei Zhong

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arXiv · 2408.00566

Kawaguchi-Silverman conjecture for int-amplified endomorphism

Sheng Meng·Guolei Zhong

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Abstract

Let $X$ be a $\mathbb{Q}$-factorial klt projective variety admitting an int-amplified endomorphism $f$, i.e., the modulus of any eigenvalue of $f^*|_{\text{NS}(X)}$ is greater than $1$. We prove Kawaguchi-Silverman conjecture for $f$ and also any other surjective endomorphism of $X$: the first dynamical degree equals the arithmetic degree of any point with Zariski dense orbit. This generalizes an early result of Kawaguchi and Silverman for the polarized $f$ case, i.e., $f^*|_{\text{NS}(X)}$ is diagonalizable with all eigenvalues of the same modulus greater than $1$.

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BibTeX RIS

Sheng Meng, Guolei Zhong. 2024-08-01. Kawaguchi-Silverman conjecture for int-amplified endomorphism. https://arxiv.org/abs/2408.00566

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