Abstract
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 ,\( \mathbb{A}_n ,n \geqslant 15 \) 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.
Partially supported by DGES PB97-0284-C02-02.
Partially supported by DGES PB97-0284-C02-01.
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Artal Bartolo, E., Carmona Ruber, J., Cogolludo Agustín, J.I. (2002). On Sextic Curves with Big Milnor Number. In: Libgober, A., Tibăr, M. (eds) Trends in Singularities. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8161-6_1
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DOI: https://doi.org/10.1007/978-3-0348-8161-6_1
Publisher Name: Birkhäuser, Basel
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