On compactifications of Mg,n with colliding markings

• Vance Blankers ^[1] ; Sebastian Bozlee ^[2]
  1. [1] Northeastern University

     Northeastern University

     City of Boston, Estados Unidos

     
  2. [2] Fordham University

     Fordham University

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 5, 2024
• Idioma: inglés
• DOI: 10.1007/s00029-024-00994-8
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we study all ways of constructing modular compactifications of the moduli space Mg,n of n-pointed smooth algebraic curves of genus g by allowing markings to collide. We find that for any such compactification, collisions of markings are controlled by a simplicial complex which we call the collision complex. Conversely, we identify modular compactifications of Mg,n with essentially arbitrary collision complexes, including complexes not associated to any space of weighted pointed stable curves. These moduli spaces classify the modular compactifications of Mg,n by nodal curves with smooth markings as well as the modular compactifications of M1,n with Gorenstein curves and smooth markings. These compactifications generalize previous constructions given by Hassett, Smyth, and Bozlee–Kuo–Neff.

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