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Award ID contains: 1701704

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  1. (, Geometry & Topology)
    Free, publicly-accessible full text available January 1, 2026
  2. ; (, International Mathematics Research Notices)
    Abstract Projective duality identifies the moduli spaces $$\textbf{B}_n$$ and $$\textbf{X}(3,n)$$ parametrizing linearly general configurations of $$n$$ points in $$\mathbb{P}^2$$ and $$n$$ lines in the dual $$\mathbb{P}^2$$, respectively. The space $$\textbf{X}(3,n)$$ admits Kapranov’s Chow quotient compactification $$\overline{\textbf{X}}(3,n)$$, studied also by Lafforgue, Hacking, Keel, Tevelev, and Alexeev, which gives an example of a KSBA moduli space of stable surfaces: it carries a family of certain reducible degenerations of $$\mathbb{P}^2$$ with $$n$$ “broken lines”. Gerritzen and Piwek proposed a dual perspective, a compact moduli space parametrizing certain reducible degenerations of $$\mathbb{P}^2$$ with $$n$$ smooth points. We investigate the relation between these approaches, answering a question of Kapranov from 2003. 
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  3. ; (, Transformation Groups)
    Full Text Available 
  4. ; (, Algebraic geometry)
    null (Ed.)
    Accepted Manuscript Full Text Available
  5. ; (, Épijournal de géométrie algébrique)
    null (Ed.)
    Accepted Manuscript Full Text Available