The local-global principle for symmetric determinantal representations of smooth plane curves in characteristic two

2014/12/29 by Yasuhiro Ishitsuka, Ishitsuka, Yasuhiro, Tetsushi Ito +1
Computer Science · Mathematics · #11D41 (Secondary) #14F22 #14G17 #14H50 (Primary) #14K15 #14K30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1412.8343

openalex publication_date 2014/12/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We give an application of Mumford's theory of canonical theta characteristics to a Diophantine problem in characteristic two. We prove that a smooth plane curve over a global field of characteristic two is defined by the determinant of a symmetric matrix with entries in linear forms in three variables if and only if such a symmetric determinantal representation exists everywhere locally. It is a special feature in characteristic two because analogous results are not true in other characteristics.

Citations

• Orbit parametrizations of theta characteristics on hypersurfaces over\n arbitrary fields
• A positive proportion of cubic curves over Q admit linear determinantal\n representations
• The local-global principle for symmetric determinantal representations of smooth plane curves

Related

• The local-global principle for symmetric determinantal representations of smooth plane curves
• A positive proportion of cubic curves over Q admit linear determinantal\n representations
• Discriminants of cubic curves and determinantal representations
• Ulrich sheaves and determinantal representations for higher secant varieties of curves
• Local Euler obstructions for determinantal varieties