A remark on the rank of finite $p$-groups of birational automorphisms

TL;DR

This paper refines the understanding of the maximum size of finite p-subgroups within the birational automorphism groups of rationally connected varieties, confirming the sharpness of bounds in many cases.

Contribution

It improves existing bounds on the rank of finite p-subgroups of birational automorphism groups and confirms their sharpness through known examples.

Findings

Improved bounds on the rank of finite p-subgroups

Validation of bounds' sharpness with known examples

Enhanced understanding of automorphism groups in algebraic geometry

Abstract

We improve a result of Prokhorov and Shramov on the rank of finite $p$-subgroups of the birational automorphism group of a rationally connected variety. Known examples show that they are sharp in many cases.