English

Explicit linear pfaffian representations of plane curves up to degree 5

Algebraic Geometry 2017-12-12 v1

Abstract

Let R be a commutative ring with 1. We prove that every homogeneous polynomial f(x_0,x_1,x_2) in R[x_0,x_1,x_2] up to degree 5 admits a linear Pfaffian R-representation. We believe that conceptually we give the shortest self-contained proof possible: we exhibit explicitly such a representation. In this sense, we generalize (up to degree 5) a result due to A. Beauville about the existence of Pfaffian representations for any smooth plane curve of any degree.

Keywords

Cite

@article{arxiv.1712.03600,
  title  = {Explicit linear pfaffian representations of plane curves up to degree 5},
  author = {David Oscari},
  journal= {arXiv preprint arXiv:1712.03600},
  year   = {2017}
}

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5 pages