A Note on Categorical Entropy of Bielliptic Surfaces and Enriques Surfaces
Algebraic Geometry
2026-05-05 v2 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2507.03890,
title = {A Note on Categorical Entropy of Bielliptic Surfaces and Enriques Surfaces},
author = {Tomoki Yoshida},
journal= {arXiv preprint arXiv:2507.03890},
year = {2026}
}
Comments
14 pages, 3 tables, to appear in Bull. Lond. Math. Soc.: Theorem A is strengthened