Elementary Transformations of Pfaffian Representations of Plane Curves

2009/08/25 by Anita Buckley, Buckley, Anita
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14H60 #msc:14Q05

paper · pdf · doi:10.48550/arxiv.0908.3554

24 pages, 1 figure

arxiv created 2009/08/25 · arxiv updated 2009/12/01

Abstract

Let C be a smooth curve in \PP² given by an equation F=0 of degree d. In this paper we consider elementary transformations of linear pfaffian representations of C. Elementary transformations can be interpreted as actions on a rank 2 vector bundle on C with canonical determinant and no sections, which corresponds to the cokernel of a pfaffian representation. Every two pfaffian representations of C can be bridged by a finite sequence of elementary transformations. Pfaffian representations and elementary transformations are constructed explicitly. For a smooth quartic, applications to Aronhold bundles and theta characteristics are given.

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