Dynamical Iitaka theory on Fano contractions

2025/06/19 by Meng, Sheng, Wang, Long, Yang, Tianle
Mathematics · #14E30 #14M25 #20K30 #37P55 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2506.16057

openalex publication_date 2025/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give several structure theorems for certain surjective endomorphisms on Mori fibre spaces, based on the dynamical Iitaka fibration of the ramification divisor. As an application, we prove the Kawaguchi-Silverman conjecture for projective bundles over abelian varieties or smooth projective varieties of Picard number one.

Citations

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Related

• A note on Kawaguchi-Silverman conjecture
• Iitaka fibrations for vector bundles
• Kawaguchi-Silverman conjecture for endomorphisms on several classes of varieties
• Dynamics of Projectivized Toric Vector Bundles
• On the birational geometry of Fano 4-folds