Stable pairs with a twist and gluing morphisms for moduli of surfaces

• Dori Bejleri ^[1] ; Giovanni Inchiostro ^[2]
  1. [1] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
  2. [2] University of Washington

     University of Washington

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 3, 2021
• Idioma: inglés
• DOI: 10.1007/s00029-021-00661-2
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• Resumen

  • We propose an alternative definition for families of stable pairs (X, D) over an arbitrary (possibly non-reduced) base in the case in which D is reduced, by replacing (X, D) with an appropriate orbifold pair (X,D). This definition of a stable family ends up being equivalent to previous ones, but has the advantage of being more amenable to the tools of deformation theory. Adjunction for (X,D) holds on the nose; there is no correction term coming from the different. This leads to the existence of functorial gluing morphisms for families of stable surfaces and functorial morphisms from (n+1) dimensional stable pairs to n dimensional polarized orbispaces. As an application, we study the deformation theory of some surface pairs.