Pfaffian representation of plane curves. Let \(\sf R\) be a commutative ring with 1. For every homogeneous polynomial \(\sf f(X_0,X_1,X_2)\) in \(\sf R[X_0,X_1,X_2]\) of degree \(\sf d \leq 25\), we find a explicit linear Pfaffian \(\sf R\)-representation of \(\sf f\). We describe an empirical method that leads us to find such \(\sf R\)-representations. This generalizes and constitutes an alternative proof (up to degree 25) of a result due to A. Beauville [Bea] about the existence of linear Pfaffian \(\mathbb{K}\)-representations for any smooth plane curve of degree \(\sf d \geq2\), where \(\mathbb{K}\) is an algebraically closed field of characteristic zero.
arXiv:1804.02803 [math.AG]