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Elementary transformations of pfaffian representations of plane curves

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
433
Issue
4
Identifiers
DOI: 10.1016/j.laa.2010.04.005
Keywords
  • Pfaffian Representations
  • Elementary Transformations
  • Linear Matrices
  • Polynomials In Projective Plane
  • Vector Bundles

Abstract

Abstract Let C be a smooth curve in P 2 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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