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A
generic slice of the moduli space of line arrangements
Kenneth Ascher and Patricio Gallardo |
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Vol. 12 (2018), No. 4, 751–778
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Abstract |
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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. |
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Keywords
moduli spaces, hyperplane arrangements, chow quotient,
wonderful compactifications, stable pairs, birational
geometry, minimal model program
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Mathematical Subject Classification 2010
Primary: 14J10
Secondary: 14D20
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Milestones
Received: 13 March 2016
Revised: 11 August 2017
Accepted: 17 March 2018
Published: 11 July 2018
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Authors |
| Kenneth Ascher | |
| Mathematics Department Massachusetts Institute of Technology Cambridge, MA United States |
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| Patricio Gallardo | |
| Department of Mathematics Washington University in St. Louis St. Louis, MO United States |
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