# Moscow Mathematical Journal

Volume 21, Issue 2, April–June 2021  pp. 401–412.

Categorical vs Topological Entropy of Autoequivalences of Surfaces

Authors:  Dominique Mattei (1)
Author institution:(1) Institut de Mathématiques de Toulouse; UMR5219, UPS, F-31062 Toulouse Cedex 9, France

Summary:

In this paper, we give an example of an autoequivalence with positive categorical entropy (in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich) for any surface containing a $(-2)$-curve. Then we show that this equivalence gives another counter-example to a conjecture proposed by Kikuta and Takahashi. In a second part, we study the action on cohomology induced by spherical twists composed with standard autoequivalences on a surface $S$ and show that their spectral radii correspond to the topological entropy of the corresponding automorphisms of $S$.

2020 Math. Subj. Class. 14F08

Keywords: Categorical entropy, derived categories, projective surfaces.