Plane curves whose singular points are cusps

Author:
Hisao Yoshihara

Journal:
Proc. Amer. Math. Soc. **103** (1988), 737-740

MSC:
Primary 14H20; Secondary 14H45

DOI:
https://doi.org/10.1090/S0002-9939-1988-0947648-8

MathSciNet review:
947648

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Abstract: Let be an irreducible curve of degree in the complex projective plane. We assume that each singular point is a one place point with multiplicity 2 or 3. Let be the sum of "the Milnor numbers" of the singularities. Then we shall show that . This gives a necessary condition for the existence of such a curve, for example, if is rational, then .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0947648-8

Keywords:
Plane curve,
cusp,
Milnor number

Article copyright:
© Copyright 1988
American Mathematical Society