Entropy of an autoequivalence on Calabi-Yau manifolds

Abstract

We prove that the categorical entropy of the autoequivalence $T_{\mathcal{O}}\circ (-\otimes \mathcal{O}(-1))$ on a Calabi-Yau manifold is the unique positive real number $\lambda$ satisfying $$\sum _{k\ge 1}\frac{\chi (\mathcal{O}(k))}{e^{k\lambda }}=e^{(d-1)t}.$$ We then use this result to construct the first counterexamples of a conjecture on categorical entropy by Kikuta and Takahashi.

10 pages. Comments are welcome!

References in corpus (4)

• 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
• Categorical entropy for Fourier-Mukai transforms on generic abelian surfaces

Cited by in corpus (2)

• A note on entropy of auto-equivalences: lower bound and the case of orbifold projective lines
• On the categorical entropy and the topological entropy