I want to calculate the fundamental group of the complement some collection of plane curves (specifically, two nodal cubics in a general position).


I've read about Severi problem (solved by Harris), which states that complement of every reduced irreducible nodal plane curve has an abelian fundamental group. I've understood the idea of the argument (deforming the picture to the arrangement of lines, which only increases the fundamental group).


I think the same (the fact that the complement has an abelian fundamental group) should hold without irreducibility assumption (i.e., for an arrangement of nodal curves which also intersect transversely). Is it true? Is it known?



Fundamental group of the complement of the arrangement of plane nodal curves
As suggested, I write my comment as an answer: the result is actually due to Fulton (*On the fundamental group of the complement of a nodal curve*, Ann. of Math. 111, no. 2 (1980), 407-409), and it is valid with no irreducibility assumption. Fulton works with the *algebraic* fundamental group; the case of the topological fundamental group was done by Deligne (Séminaire Bourbaki 1979/80, Exp.543, pp. 1-10.


