Plane curves as Pfaffians

Buckley, Anita; Košir, Tomaž

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 2, pp. 363-388.

Let $C$ be a smooth curve in ${\mathbb{P}}^2$ 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.

Classification : 14H60, 14D20, 15A15, 15A54

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