Dynamical Iitaka theory on Fano contractions
Sheng Meng, Long Wang, Tianle Yang
TL;DR
This paper develops structure theorems for specific endomorphisms on Mori fiber spaces using dynamical Iitaka fibrations and proves the Kawaguchi-Silverman conjecture in particular cases involving projective bundles.
Contribution
It introduces new structure theorems based on dynamical Iitaka fibrations and verifies the Kawaguchi-Silverman conjecture for certain projective bundles.
Findings
Established structure theorems for endomorphisms on Mori fiber spaces.
Proved the Kawaguchi-Silverman conjecture for projective bundles over specific varieties.
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology