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On sextic curves with big Milnor number. (English) Zbl 1018.14009

Libgober, Anatoly (ed.) et al., Trends in singularities. Basel: Birkhäuser. Trends in Mathematics. 1-29 (2002).
Summary: We present an exhaustive description, up to projective isomorphism, of all irreducible sextic curves in \(\mathbb P^2\) having a singular point of type \(\mathbb A_n\), \(n\geq 15\), 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.
For the entire collection see [Zbl 0997.00011].

MSC:

14H50 Plane and space curves
14H20 Singularities of curves, local rings
14H51 Special divisors on curves (gonality, Brill-Noether theory)
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