If we regard a set of s lines in P2\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb P}^2$$\end{document} over either the reals or the complex numbers as an algebraic plane curve, then it is an open problem to classify for all s those for which the number t2\documentclass[12pt]{minimal}
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\begin{document}$$t_2$$\end{document} of points of multiplicity 2 satisfies t2<⌊s/2⌋\documentclass[12pt]{minimal}
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\begin{document}$$t_2<\lfloor s/2\rfloor $$\end{document}. By the Sylvester–Gallai theorem, there are no nontrivial (i.e., not a pencil or a near pencil) real arrangements with t2=0\documentclass[12pt]{minimal}
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\begin{document}$$t_2=0$$\end{document}, but there are complex arrangements with t2=0\documentclass[12pt]{minimal}
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\begin{document}$$t_2=0$$\end{document} and it is an open problem to classify them. In this paper, we initiate a classification of an interesting class of line arrangements called the supersovable line arrangements and give a partial classification for them over the reals or the complex numbers. In particular, we show that a complex line arrangement which is nontrivial cannot have more than 4 modular points and we completely describe those with 3 or 4 modular points.
