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arXiv · 1602.08958

A Generic Slice of the Moduli Space of Line Arrangements

Kenneth Ascher·Patricio Gallardo
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Abstract

We study the compactification of the locus parametrizing lines with a fixed intersection to a given line, inside the moduli space of line arrangements in the projective plane constructed for weight one by Hacking-Keel-Tevelev and Alexeev for general weights. We show that this space is smooth, with normal crossing boundary, and that it has a morphism to the moduli space of marked rational curves which can be understood as a natural continuation of the blow up construction of Kapranov. In addition, we prove that it is isomorphic to a closed subvariety inside a non-reductive Chow quotient. The parametrized objects are surfaces with broken lines, whose dual graphs are rooted trees with possibly repeated markings.

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Kenneth Ascher, Patricio Gallardo. 2017-08-19. A Generic Slice of the Moduli Space of Line Arrangements. https://doi.org/10.2140/ant.2018.12.751

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