Plane curves of fixed bidegree and their $A_k$-singularities

Julia Schneider

Plane curves of fixed bidegree and their $A_k$-singularities

Algebraic Geometry 2018-08-16 v1

Authors: Julia Schneider

Abstract

We provide a tool how one can view a polynomial on the affine plane of bidegree $(a,b)$ - by which we mean that its Newton polygon lies in the triangle spanned by $(a,0)$ , $(0,b)$ and the origin - as a curve in a Hirzebruch surface having nice geometric properties. As an application, we study maximal $A_k$ -singularities of curves of bidegree $(3,b)$ and find the answer for $b\leq 12$ .

Keywords

plane curves bidegree a_k-singularities hirzebruch surface newton polygon polynomials

Cite

@article{arxiv.1808.05133,
  title  = {Plane curves of fixed bidegree and their $A_k$-singularities},
  author = {Julia Schneider},
  journal= {arXiv preprint arXiv:1808.05133},
  year   = {2018}
}

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