A bound for the Milnor number of plane curve singularities

• Autorzy: Arkadiusz Płoski
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

Milnor number; Plane algebraic curve

Kategorie tematyczne

• 14B05: Singularities
• 14N99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 5
• Strony: 688-693

Daty

wydano

2014-05-01

online

2014-02-15

Twórcy

autor

Arkadiusz Płoski

• Kielce University of Technology

Bibliografia

• [1] Cassou-Noguès P., Płoski A., Invariants of plane curve singularities and Newton diagrams, Uni. Iagel. Acta Math., 2011, 49, 9–34
• [2] Fulton W., Algebraic Curves, Adv. Book Classics, Addison-Wesley, Redwood City, 1989
• [3] Garcia Barroso E.R., Płoski A., An approach to plane algebroid branches, preprint available at http://arxiv.org/abs/1208.0913
• [4] Greuel G.-M., Lossen C., Shustin E., Plane curves of minimal degree with prescribed singularities, Invent. Math., 1998, 133(3), 539–580 http://dx.doi.org/10.1007/s002220050254
• [5] Gusein-Zade S.M., Nekhoroshev N.N., Singularities of type A k on plane curves of a chosen degree, Funct. Anal. Appl., 2000, 34(3), 214–215 http://dx.doi.org/10.1007/BF02482412
• [6] Gwozdziewicz J., Płoski A., Formulae for the singularities at infinity of plane algebraic curves, Univ. Iagel. Acta Math., 2001, 39, 109–133
• [7] Huh J., Milnor numbers of projective hypersurfaces with isolated singularities, preprint available at http://arxiv.org/abs/1210.2690
• [8] Teissier B., Resolution Simultanée I, II, In: Séminaire sur les Singularités des Surfaces, Lecture Notes in Math., 777, Springer, Berlin, 1980, 71–146 http://dx.doi.org/10.1007/BFb0085880
• [9] Wall C.T.C., Singular Points of Plane Curves, London Math. Soc. Stud. Texts, 63, Cambridge University Press, Cambridge, 2004 693

Identyfikatory

DOI

10.2478/s11533-013-0378-6