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arXiv · 1808.05133

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

Julia Schneider
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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 $b\leq 12$.

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Julia Schneider. 2018-08-15. Plane curves of fixed bidegree and their $A_k$-singularities. https://arxiv.org/abs/1808.05133

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