## Plane curves whose singular points are cusps

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- by Hisao Yoshihara
- Proc. Amer. Math. Soc.
**103**(1988), 737-740 - DOI: https://doi.org/10.1090/S0002-9939-1988-0947648-8
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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 $d \leq 10$.## References

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*A note on the existence of some curves*, (to appear).

## Bibliographic Information

- © Copyright 1988 American Mathematical Society
- 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