2024/03/12 by She Yang, Yang, She
Computer Science · Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2403.07394
openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be an algebraically closed field of arbitrary characteristic and let X be an irreducible projective variety over K. Let G\subseteqBir(X) be a bounded-degree subgroup. We prove that there exists an irreducible projective variety Y birational to X, such that every element of G becomes an automorphism of Y after the birational transformation. If K=ℂ, this result is stated in [Can14, Theorem 2.5] and the proof backs to [HZ96, Section 5]. The proof in [HZ96] is not purely algebraic. Inheriting the methods in [HZ96], we give a purely algebraic proof of this statement in arbitrary characteristic. We will also discuss a corollary of this result which is useful in arithmetic dynamics.