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arXiv · 2507.03890

A Note on Categorical Entropy of Bielliptic Surfaces and Enriques Surfaces

Tomoki Yoshida
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Abstract

In this note, we show that there exists an autoequivalence of positive categorical entropy on the derived category of bielliptic surfaces. This gives the first example of a surface admitting positive categorical entropy in the absence of both positive topological entropy and any spherical objects. Moreover, we prove a Gromov-Yomdin type equality for the categorical entropy of autoequivalences on bielliptic surfaces and give a counterexample to this equality on Enriques surfaces.

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Tomoki Yoshida. 2025-07-05. A Note on Categorical Entropy of Bielliptic Surfaces and Enriques Surfaces. https://arxiv.org/abs/2507.03890

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