Plane curves as Pfaffians

2008/05/19 by Anita Buckley, Buckley, Anita, Tomaz Kosir +2
Computer Science · Engineering · Mathematics · #14H50 #14H60 #15A21 #15A57 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Computational Geometry and Mesh Generation #FOS: Mathematics #math.AG #msc:14H50 #msc:14H60 #msc:15A21 #msc:15A57

paper · pdf · doi:10.48550/arxiv.0805.2831

16 pages, 1 figure

arxiv created 2008/05/19 · openalex publication_date 2008/05/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be a smooth curve in \PP² given by an equation F=0 of degree d. In this paper we parametrise all linear pfaffian representations of F by an open subset in the moduli space M_C(2,K_C). We construct an explicit correspondence between pfaffian representations of C and rank 2 vector bundles on C with canonical determinant and no sections.

Citations

• Vector bundles on curves and generalized theta functions: recent results and open problems

Related

• Elementary Transformations of Pfaffian Representations of Plane Curves
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