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

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Borodzik, Maciej
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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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Mathematics - Algebraic Geometry, 14H50, 14H20, 32S50, 14E15
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