Nontrivial complex supersolvable line arrangements have at most 4 modular points and none when all crossings have multiplicity 3 or 4.
Melchior, Über Vielseite der projektiven Ebene, Deu tsche Math
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Real and complex supersolvable line arrangements in the projective plane
Nontrivial complex supersolvable line arrangements have at most 4 modular points and none when all crossings have multiplicity 3 or 4.