Plane curves whose singular points are cusps

Yoshihara, Hisao

doi:10.1090/S0002-9939-1988-0947648-8

Plane curves whose singular points are cusps
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Proc. Amer. Math. Soc. 103 (1988), 737-740 Request permission

Abstract:

Let $C$ be an irreducible curve of degree $d$ in the complex projective plane. We assume that each singular point is a one place point with multiplicity 2 or 3. Let $\sigma$ be the sum of "the Milnor numbers" of the singularities. Then we shall show that $7\sigma < 6{d^2} - 9d$. This gives a necessary condition for the existence of such a curve, for example, if $C$ is rational, then $d \leq 10$.

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A note on the existence of some curves

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