Real and complex supersolvable line arrangements in the projective plane
We study supersolvable line arrangements in ${\mathbb P}^2$ over the reals and over the complex numbers, as the first step toward a combinatorial classification. Our main results show that a nontrivial (i.e., not a pencil or near pencil) complex line arrangement cannot have more than 4 modular points, and if all of the crossing points of a complex line arrangement have multiplicity 3 or 4, then the arrangement must have 0 modular points (i.e., it cannot be supersolvable). This provides at least a little evidence for our conjecture that every nontrivial complex supersolvable line arrangement has at least one point of multiplicity 2, which in turn is a step toward the much stronger conjecture of Anzis and Toh\v{a}neanu that every nontrivial complex supersolvable line arrangement with $s$ lines has at least $s/2$ points of multiplicity 2.
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Krishna Hanumanthu (add twitter)
Brian Harbourne (add twitter)
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Mathematics - Algebraic Geometry

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07/18/19 06:05PM
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mathAGb: Krishna Hanumanthu, Brian Harbourne : Real and complex supersolvable line arrangements in the projective plane https://t.co/sAnbAPouRL https://t.co/ytdVXaKyX6
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