Bijective Cremona transformations of the plane

• Shamil Asgarli ^[1] ; Kuan-Wen Lai ^[3] ; Masahiro Nakahara ^[2] ; Susanna Zimmermann ^[4]
  1. [1] University of British Columbia

     University of British Columbia

     Canadá

     
  2. [2] University of Washington

     University of Washington

     Estados Unidos

     
  3. [3] Universität Bonn, Germany
  4. [4] Univ Angers, France

  Mostrar afiliaciones +
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 3, 2022
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We study the birational self-maps of the projective plane over finite fields that induce permutations on the set of rational points. As a main result, we prove that no odd permutation arises over a non-prime finite field of characteristic two, which completes the investigation initiated by Cantat about which permutations can be realized this way. Main ingredients in our proof include the invariance of parity under groupoid conjugations by birational maps, and a list of generators for the group of such maps.