On entropy of spherical twists

TL;DR

This paper investigates the entropy of spherical twists in derived categories, confirming a Gromov-Yomdin type conjecture for them, providing counterexamples in higher dimensions, and exploring the structure of spherical objects in K3 surfaces.

Contribution

It proves the Gromov-Yomdin type conjecture for spherical twists and constructs counterexamples in higher-dimensional Calabi-Yau manifolds, advancing understanding of categorical entropy.

Findings

Gromov-Yomdin type conjecture holds for spherical twists

Counterexamples found for higher-dimensional Calabi-Yau manifolds

Non-emptiness of complements of spherical objects in K3 surfaces

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.