On the automorphism group of rational manifolds

TL;DR

This paper proves that automorphisms of certain rational manifolds, constructed via blow-ups of projective space, have zero topological entropy, indicating they lack complex chaotic behavior.

Contribution

It establishes a new result linking the structure of rational manifolds obtained through blow-ups to the entropy of their automorphisms.

Findings

Automorphisms of these rational manifolds have zero topological entropy.

The result applies to manifolds obtained from projective space by specific blow-ups.

The proof connects geometric construction with dynamical complexity.

Abstract

In this note, we prove that every automorphism of a rational manifold which is obtained from $\Bbb{P}^k$ by a finite sequence blow-ups along smooth centers of dimension at most r with k>2r+2 has zero topological entropy.