Rational self-maps of projective surfaces with a regular iterate

2025/09/05 by Sina Saleh, Saleh, Sina
Mathematics · #Advanced Topics in Algebra #Rings, Modules, and Algebras #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2509.05194

Abstract

We show that if Φ: X \dashrightarrow X is a dominant rational self-map of a projective surface X over ℂ with a regular and non-invertible iterate Φⁿ, then we can take n ≤ 12. This bound is sharp and realized on X = ℙ². In the case where Φ is a birational self-map of ℙ² we prove that as long as Φ does not preserve a non-constant fibration, if some iterate Φⁿ is regular then Φ itself must be regular.

Citations

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Related

• Rational self-maps with a regular iterate on a semiabelian variety
• Self Rational Maps of K3 Surfaces
• Degrees of Iterates of Rational Maps on Normal Projective Varieties
• Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties
• Rational maps and K3 surfaces