A generic slice of the moduli space of line arrangements

Ascher, Kenneth; Gallardo, Patricio

doi:10.2140/ant.2018.12.751

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A generic slice of the moduli space of line arrangements

Kenneth Ascher and Patricio Gallardo

Vol. 12 (2018), No. 4, 751–778

DOI: 10.2140/ant.2018.12.751

Abstract

We study the compactification of the locus parametrizing lines having a fixed intersection with a given line, inside the moduli space of line arrangements in the projective plane constructed for weight one by Hacking, Keel and Tevelev and for general weights by Alexeev. 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 our space is isomorphic to a closed subvariety inside a nonreductive Chow quotient.

Keywords

moduli spaces, hyperplane arrangements, chow quotient, wonderful compactifications, stable pairs, birational geometry, minimal model program

Mathematical Subject Classification 2010

Primary: 14J10

Secondary: 14D20

Milestones

Received: 13 March 2016

Revised: 11 August 2017

Accepted: 17 March 2018

Published: 11 July 2018

Authors

Kenneth Ascher
Mathematics Department Massachusetts Institute of Technology Cambridge, MA United States

Patricio Gallardo
Department of Mathematics Washington University in St. Louis St. Louis, MO United States

Vol. 12, No. 4, 2018