On Hilbert modular threefolds of discriminant 49

• Lev A. Borisov ^[1] ; Paul E. Gunnells ^[2]
  1. [1] Rutgers University

     Rutgers University

     City of New Brunswick, Estados Unidos

     
  2. [2] University of Massachusetts Amherst

     University of Massachusetts Amherst

     Town of Amherst, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 19, Nº. 4, 2013, págs. 923-947
• Idioma: inglés
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• Resumen

  • Let KK be the totally real cubic field of discriminant 4949 , let OO be its ring of integers, and let p⊂Op⊂O be the prime over 77 . Let Γ(p)⊂Γ=SL2(O)Γ(p)⊂Γ=SL2(O) be the principal congruence subgroup of level pp . This paper investigates the geometry of the Hilbert modular threefold attached to Γ(p)Γ(p) and some related varieties. In particular, we discover an octic in P3P3 with 8484 isolated singular points of type A2A2 .