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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


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.

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