Work

Arithmetic degree and its application to Zariski dense orbit conjecture

Year: 2025

Type: article

Abstract: We prove that for a dominant rational self‐map on a quasi‐projective variety defined over , there is a point whose ‐orbit is well‐defined and its arithmetic degree is arbitrarily close to the first dynamical degree of . As an application, we prove that Zariski dense orbit conjecture holds for a birational map defined over whose first dynamical degree is strictly larger than its third dynamical degree. In particular, the conjecture holds for birational maps on threefolds whose first dynamical is degree greater than 1.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70282

Authors: Yohsuke Matsuzawa, Junyi Xie

Institutions: Osaka Metropolitan University, Peking University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Japan Society for the Promotion of Science

Awards: G576856182, 代数多様体の数論力学系の研究