On entropy of spherical twists

Abstract

In this paper, we compute categorical entropy of spherical twists. In particular, we prove that Gromov-Yomdin type conjecture holds for spherical twists. Moreover, we construct counterexamples of Gromov-Yomdin type conjecture for K3 surfaces modifying Fan's construction for even higher dimensional Calabi-Yau manifolds. The appendix, by Arend Bayer, shows non-emptyness of complements of a number of spherical objects in the derived categories of K3 surfaces.

arXiv comment11 pages, With an appendix by Arend Bayer. v2: Counterexamples of Gromov-Yomdin type conjecture for K3 surfaces are improved and the appendix by A. Bayer is added

References in corpus (5)

• A note on entropy of auto-equivalences: lower bound and the case of orbifold projective lines
• On entropy for autoequivalences of the derived category of curves
• On the categorical entropy and the topological entropy
• Some aspects of explicit birational geometry inspired by complex dynamics
• Automorphisms of positive entropy on some hyperKahler manifolds via derived automorphisms of K3 surfaces

Cited by in corpus (2)

• A note on entropy of auto-equivalences: lower bound and the case of orbifold projective lines
• Categorical vs topological entropy of autoequivalences of surfaces