Linear automorphisms of smooth hypersurfaces giving Galois points

2021/01/12 by Tarō Hayashi, Hayashi, Taro · 3 citations
Mathematics · #12F10 #14J70 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2101.04797

openalex publication_date 2021/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth hypersurface X of degree d≥4 in a projective space \mathbb Pⁿ⁺¹. We consider a projection of X from p∈\mathbb Pⁿ⁺¹ to a plane H≅\mathbb Pⁿ. This projection induces an extension of function fields \mathbb C(X)/\mathbb C(\mathbb Pⁿ). The point p is called a Galois point if the extension is Galois. In this paper, we will give a necessary and sufficient conditions for X to have Galois points by using linear automorphisms.

Cited by

• Large orders of automorphisms of smooth curves in \mathbb P¹× \mathbb P¹
• Subgroups of the Projective Linear Group Realized by wild Galois Points
• Persistence of Galois property of hypersurfaces over algebraic integers across other characteristics

Related

• A hyperplane section theorem for Galois points and its application
• Persistence of Galois property of hypersurfaces over algebraic integers across other characteristics
• Hypersurfaces passing through the Galois orbit of a point
• Linear system of hypersurfaces passing through a Galois orbit
• Subgroups of the Projective Linear Group Realized by wild Galois Points