The octanomial normal forms of cubic surfaces with applications to automorphisms

2023/11/20 by China Kaneko, Kaneko, China
Mathematics · #14G17 #14J26 #14J50 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2311.11678

openalex publication_date 2023/11/20 · openalex created_date 2023/11/23 · openalex updated_date 2026/07/28

Abstract

We will show that in any characteristic every nonsingular cubic surface is projectively isomorphic to the surface given by the octanomial normal form. This normal form is discovered by M. Panizzut, E. C. Sertöz, and B. Sturmfels in 2020 only in characteristic 0 in a heavily computational way. Our proof is more conceptual and characteristic-free. As an application, we give octanomial normal forms of the strata of the coarse moduli space of cubic surfaces defined by I. Dolgachev and A. Duncan, which preserve most specialization with respect to automorphisms.

Related

• Automorphisms of cubic surfaces in positive characteristic
• Cubic Surfaces and Borcherds Products
• An automorphic form related to cubic surfaces
• The most symmetric smooth cubic surface
• Groups acting on cubic surfaces in characteristic zero