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arXiv · 0908.4500

Number of singular points of a genus $g$ curve with one point at infinity

Maciej Borodzik
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Abstract

We bound the maximal number N of singular points of a plane algebraic curve C that has precisely one place at infinity with one branch in terms of its first Betti number $b_1(C)$. Asymptotically we prove that $N<\sim{17/11}b_1(C)$ for large $b_1$. In particular, in the case of curves with one place at infinity, we confirm the Zaidenberg and Lin conjecture stating that $N\le 2b_1+1$.

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Maciej Borodzik. 2009-08-31. Number of singular points of a genus $g$ curve with one point at infinity. https://arxiv.org/abs/0908.4500

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