Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the variety of plane curves of degree $ d$ with $ \delta$ nodes and $ \kappa$ cusps


Author: Pyung-Lyun Kang
Journal: Trans. Amer. Math. Soc. 316 (1989), 165-192
MSC: Primary 14H10; Secondary 14H20
MathSciNet review: 1014468
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {{\mathbf{P}}^N}$ be the projective space which parametrizes all plane curves of degree $ d$ and $ V(d,\delta ,\kappa )$ the subvariety of $ {{\mathbf{P}}^N}$ consisting of all reduced and irreducible plane curves of degree $ d$ with $ \delta $ nodes and $ \kappa $ cusps as their only singularities. In this paper we prove that $ V(d,\delta ,\kappa )$ is irreducible if $ \kappa \leqslant 3$, except possibly when $ \kappa = 3$ and $ d = 5$ or $ 6$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 14H10, 14H20

Retrieve articles in all journals with MSC: 14H10, 14H20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-1014468-3
PII: S 0002-9947(1989)1014468-3
Keywords: Plane curves, cusps, families of plane curves with nodes and cusps
Article copyright: © Copyright 1989 American Mathematical Society