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On A_k-singularity on a plane curve of fixed degree

Sabir M. Gusein-Zade·Nikolay N. Nekhoroshev
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Abstract

Let $k(d)$ be the maximal possible integer $k$ such that there exists a plane curve of degree $d$ with an $A_k$--singularity. We construct a plane curve of degree $28s+9$ ($s\in\Z_{\ge 0}$) which has an $A_k$--singularity with $k=420s^2+269s+42$. Therefore one has $\underline{\lim}_{d\to\infty}k(d)/d^2\ge 15/28$ (pay attention that $15/28>1/2$).

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Sabir M. Gusein-Zade, Nikolay N. Nekhoroshev. 1999-06-22. On A_k-singularity on a plane curve of fixed degree. https://arxiv.org/abs/math/9906147

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