Plane curves as Pfaffians

Anita Buckley; Tomaz Kosir

Plane curves as Pfaffians

Algebraic Geometry 2008-05-20 v1

Authors: Anita Buckley , Tomaz Kosir

Abstract

Let $C$ be a smooth curve in $\PP^2$ 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.

Keywords

moduli spaces of vector bundles moduli spaces algebraic curves

Cite

@article{arxiv.0805.2831,
  title  = {Plane curves as Pfaffians},
  author = {Anita Buckley and Tomaz Kosir},
  journal= {arXiv preprint arXiv:0805.2831},
  year   = {2008}
}

Comments

16 pages, 1 figure

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