Geometric interpretation of toroidal compactifications of moduli of\n points in the line and cubic surfaces

2020/06/01 by Patricio A. Gallardo, Matt Kerr, Gallardo, Patricio +3 · 2 citations
Mathematics · #14D06 #14E05 #14J10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2006.01314

openalex publication_date 2020/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that some GIT compactifications associated to moduli spaces of\neither points in the projective line or cubic surfaces are isomorphic to\nBaily-Borel compactifications of appropriate ball quotients. In this paper, we\nshow that their respective toroidal compactifications are isomorphic to moduli\nspaces of stable pairs as defined in the context of the MMP. Moreover, we give\na precise mixed-Hodge-theoretic interpretation of this isomorphism for the case\nof eight labeled points in the projective line.\n

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