Commensurability classes of fake quadrics

• Benjamin Linowitz ^[1] ; Matthew Stover ^[2] ; John Voight ^[3]
  1. [1] Oberlin College

     Oberlin College

     City of Oberlin, Estados Unidos

     
  2. [2] Temple University

     Temple University

     City of Philadelphia, Estados Unidos

     
  3. [3] Dartmouth College

     Dartmouth College

     Town of Hanover, Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 3, 2019
• Idioma: inglés
• DOI: 10.1007/s00029-019-0492-9
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  • Texto completo (pdf)
• Resumen

  • A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classification of all irreducible fake quadrics according to the commensurability class of their fundamental group. To accomplish this task, we develop a number of new techniques that explicitly bound the arithmetic invariants of a fake quadric and more generally of an arithmetic manifold of bounded volume arising from a form of {{\,\mathrm{SL}\,}}_2 over a number field.