Orbit parametrizations of theta characteristics on hypersurfaces over\n arbitrary fields

2014/12/22 by Yasuhiro Ishitsuka, Ishitsuka, Yasuhiro · 3 citations
Mathematics · #14G17 #14J50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Primary 14M10 #Secondary 11E04

paper · pdf · doi:10.48550/arxiv.1412.6978

openalex publication_date 2014/12/22 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28

Abstract

It is well-known that theta characteristics on smooth plane curves over a\nfield of characteristic different from two are in bijection with certain smooth\ncomplete intersections of three quadrics. We generalize this bijection to\npossibly singular hypersurfaces of any dimension over arbitrary fields\nincluding those of characteristic two. It is accomplished in terms of linear\norbits of tuples of symmetric matrices instead of smooth complete intersections\nof quadrics. As an application of our methods, we give a description of the\nprojective automorphism groups of complete intersections of quadrics\ngeneralizing Beauville's results.\n

Cited by

• The local-global principle for symmetric determinantal representations of smooth plane curves
• The local-global principle for symmetric determinantal representations of smooth plane curves in characteristic two
• Linear determinantal representations of smooth plane cubics over finite\n fields

Related

• Orbits of Theta Characteristics
• Linear orbits of smooth quadric surfaces
• Intersections of Real Symmetric Hypersurfaces
• On intersections of symmetric determinantal varieties and theta characteristics of canonical curves
• Characterizing Curves by their odd Theta-characteristics