@article{9524aa0f0d0c41b4bc45902223ec7171,

title = "A generic slice of the moduli space of line arrangements",

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 = "Birational geometry, Chow quotient, Hyperplane arrangements, Minimal model program, Moduli spaces, Stable pairs, Wonderful compactifications",

author = "Kenneth Ascher and Patricio Gallardo",

note = "Funding Information: We would like to thank Dan Abramovich, Valery Alexeev, Dori Bejleri, Noah Giansiracusa, Paul Hacking, Brendan Hassett, Sean Keel, Steffen Marcus, and Dhruv Ranganathan for insightful discussions. We thank the referees for their suggestions which greatly helped improve our work. Ascher especially thanks Steffen Marcus for help understanding deformation theory leading to the proof of Lemma 4.9. Research of Gallardo is supported in part by funds from NSFNational Sleep Foundation grant DMS-1344994 of the RTG in Algebra, Algebraic Geometry, and Number Theory, at the University of Georgia. Ascher is supported in part by funds from NSFNational Sleep Foundation grant DMS-1500525 grant, NSFNational Sleep Foundation grant DMS-1162367, and an NSF postdoctoral fellowship. Funding Information: We would like to thank Dan Abramovich, Valery Alexeev, Dori Bejleri, Noah Giansiracusa, Paul Hacking, Brendan Hassett, Sean Keel, Steffen Marcus, and Dhruv Ranganathan for insightful discussions. We thank the referees for their suggestions which greatly helped improve our work. Ascher especially thanks Steffen Marcus for help understanding deformation theory leading to the proof of Lemma 4.9. Research of Gallardo is supported in part by funds from NSF grant DMS-1344994 of the RTG in Algebra, Algebraic Geometry, and Number Theory, at the University of Georgia. Ascher is supported in part by funds from NSF grant DMS-1500525 grant, NSF grant DMS-1162367, and an NSF postdoctoral fellowship. Publisher Copyright: {\textcopyright} 2018 Mathematical Sciences Publishers.",

year = "2018",

doi = "10.2140/ant.2018.12.751",

language = "English (US)",

volume = "12",

pages = "751--778",

journal = "Algebra and Number Theory",

issn = "1937-0652",

publisher = "Mathematical Sciences Publishers",

number = "4",

}