2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161269Let $C$ 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.16 pages, 1 figureAlgebraic Geometry14H60, 14H50, 15A57, 15A21text