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arXiv · 2110.12597

On Gromov-Yomdin type theorems and a categorical interpretation of holomorphicity

Federico Barbacovi·Jongmyeong Kim
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Abstract

In topological dynamics, the Gromov--Yomdin theorem states that the topological entropy of a holomorphic automorphism $f$ of a smooth projective variety is equal to the logarithm of the spectral radius of the induced map $f^*$. In order to establish a categorical analogue of the Gromov--Yomdin theorem, one first needs to find a categorical analogue of a holomorphic automorphism. In this paper, we propose a categorical analogue of a holomorphic automorphism and prove that the Gromov--Yomdin type theorem holds for them.

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Federico Barbacovi, Jongmyeong Kim. 2021-10-25. On Gromov-Yomdin type theorems and a categorical interpretation of holomorphicity. https://arxiv.org/abs/2110.12597

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