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arXiv · 1804.02803

Pfaffian representations of plane curves

David Oscari
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Abstract

Let R be a commutative ring with 1. For every homogeneous polynomial f(X_0,X_1,X_2) in R[X_0,X_1,X_2] of degree d <= 25, we find a explicit linear Pfaffian R-representation of f. We describe an empirical method that leads us to find such 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 K-representations for any smooth plane curve of degree d >= 2, where K is an algebraically closed field of characteristic zero.

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David Oscari. 2018-04-09. Pfaffian representations of plane curves. https://arxiv.org/abs/1804.02803

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