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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo

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Volume 12, Issue 5


Volume 13 (2015)

A bound for the Milnor number of plane curve singularities

Arkadiusz Płoski
  • Department of Mathematics, Kielce University of Technology, Al. Tysiąclecia Państwa Polskiego 7, 25-314, Kielce, Poland
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Published Online: 2014-02-15 | DOI: https://doi.org/10.2478/s11533-013-0378-6


Let f = 0 be a plane algebraic curve of degree d > 1 with an isolated singular point at 0 ∈ ℂ2. We show that the Milnor number μ0(f) is less than or equal to (d−1)2 − [d/2], unless f = 0 is a set of d concurrent lines passing through 0, and characterize the curves f = 0 for which μ0(f) = (d−1)2 − [d/2].

Keywords: Milnor number; Plane algebraic curve

MSC: 14B05; 14N99

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About the article

Published Online: 2014-02-15

Published in Print: 2014-05-01

Citation Information: Open Mathematics, Volume 12, Issue 5, Pages 688–693, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0378-6.

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© 2014 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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