Plane curves as Pfaffians

Details Plane curves as Pfaffians Plane curves as Pfaffians

2008-05-19

arxiv.org/abs/0805.2831v1

Mathematics

Algebraic Geometry

16 pages, 1 figure

Scientific paper

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.

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