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Proceedings of the American Mathematical Society

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A note on the variety of plane curves with nodes and cusps


Author: Pyung-Lyun Kang
Journal: Proc. Amer. Math. Soc. 106 (1989), 309-312
MSC: Primary 14H10; Secondary 14H20
DOI: https://doi.org/10.1090/S0002-9939-1989-0952316-3
MathSciNet review: 952316
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Abstract: Let $ {\mathbb{P}^N}$ be the projective space of all degree $ d$ plane curves and $ V(d,\delta ,\kappa )$ the subvariety of $ {\mathbb{P}^N}$ consisting of all reduced and irreducible curves with $ \delta $ notes and $ \kappa $ cusps. Then $ V(d,\delta ,\kappa )$ is irreducible if $ \kappa \leq \frac{1}{2}(d + 1) - g$.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0952316-3
Keywords: Plane curves, cusps, families of plane curves with nodes and cusps
Article copyright: © Copyright 1989 American Mathematical Society

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