On polynomial automorphisms of Nagata type

2024/01/23 by Jorge A. C. Huarcaya, Huarcaya, Jorge A. C., Joe Palacios +1
Chemistry · Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Carbohydrate Chemistry and Synthesis #Commutative Algebra (math.AC) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2401.12523

openalex publication_date 2024/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We define a family of polynomial ring homomorphisms generalizing the well-known Nagata automorphism. We establish necessary and sufficient conditions under which these homomorphisms are automorphisms, and verify that they satisfy the Jacobian conjecture. Additionally, we provide a necessary condition within this family to obtain wild automorphisms, and independently derive a property related to the upper semicontinuity of the Łojasiewicz exponent at infinity.

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