Let $C$ be a smooth curve in $\PP^2$ given by an equation F=0 of degree $d$.In this paper we consider elementary transformations of linear pfaffianrepresentations of $C$. Elementary transformations can be interpreted asactions on a rank 2 vector bundle on $C$ with canonical determinant and nosections, which corresponds to the cokernel of a pfaffian representation. Everytwo pfaffian representations of $C$ can be bridged by a finite sequence ofelementary transformations. Pfaffian representations and elementarytransformations are constructed explicitly. For a smooth quartic, applicationsto Aronhold bundles and theta characteristics are given.
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机译：令$ C $是$ \ PP ^ 2 $中由度d $$的方程F = 0给出的平滑曲线。在本文中，我们考虑$ C $的线性pfaffian表示的基本变换。可以将基本转换解释为对具有标准行列式和nosections的$ C $上第2级向量束的操作，这对应于pfaffian表示的色差。 $ C $的每两个pfaffian表示可以通过有限顺序的基本转换来桥接。 Pfaffian表示和基本转换是明确构造的。对于平滑四次，给出了对Aronhold束和theta特性的应用。
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