On entropy of $\mathbb{P}$-twists

TL;DR

This paper investigates the entropy properties of $bP$-twists and spherical twists in derived categories, revealing that $bP$-twists are not conjugate to standard autoequivalences and computing their categorical entropy functions.

Contribution

It demonstrates that $bP$-twists are not conjugate to standard autoequivalences and calculates their categorical entropy, advancing understanding of autoequivalence dynamics.

Findings

$bP$-twists are not conjugate to standard autoequivalences

Categorical entropy functions of $bP$-twists are computed

Categorical polynomial entropy of spherical and $bP$-twists is determined

Abstract

We show that the $\mathbb{P}$-twist associated to any $\mathbb{P}$-object of a smooth project variety is not conjugate to a standard autoequivalence. This result is obtained by computing the categorical entropy functions of $\mathbb{P}$-twists. We also determine the categorical polynomial entropy of spherical twists and $\mathbb{P}$-twists, under an additional assumption.