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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Plane curves whose singular points are cusps


Author: Hisao Yoshihara
Journal: Proc. Amer. Math. Soc. 103 (1988), 737-740
MSC: Primary 14H20; Secondary 14H45
MathSciNet review: 947648
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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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DOI: https://doi.org/10.1090/S0002-9939-1988-0947648-8
Keywords: Plane curve, cusp, Milnor number
Article copyright: © Copyright 1988 American Mathematical Society