A generic slice of the moduli space of line arrangements

Kenneth Ascher, Patricio Gallardo

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)751-778
Number of pages28
JournalAlgebra and Number Theory
Volume12
Issue number4
DOIs
StatePublished - Jan 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Birational geometry
  • Chow quotient
  • Hyperplane arrangements
  • Minimal model program
  • Moduli spaces
  • Stable pairs
  • Wonderful compactifications

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