On sextic curves with big Milnor number.



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Artal Bartolo, Enrique and Carmona Ruber, Jorge and Cogolludo Agustín, José Ignacio (2002) On sextic curves with big Milnor number. In Trends in Singularities. Birkhäuser Basel, USA, pp. 1-29. ISBN 978-3-0348-9461-6

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Official URL: http://link.springer.com/chapter/10.1007/978-3-0348-8161-6_1


In this work we present an exhaustive description, up to projective isomorphism, of all irreducible sextic curves in ℙ2 having a singular point of type , A n ,n⩾15 n ≥ 15, only rational singularities and global Milnor number at least 18. Moreover, we develop a method for an explicit construction of sextic curves with at least eight — possibly infinitely near — double points. This method allows us to express such sextic curves in terms of arrangements of curves with lower degrees and it provides a geometric picture of possible deformations. Because of the large number of cases, we have chosen to carry out only a few to give some insights into the general situation.

Item Type:Book Section
Uncontrolled Keywords:Equisingular family; Sextic curves; Deformation; Fundamental group
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:22480
Deposited On:22 Jul 2013 08:21
Last Modified:02 Sep 2020 10:19

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