Abstract:
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 $S$.
Key words and phrases:categorical entropy, derived categories, projective surfaces.
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