Two kinds of real lines on real del Pezzo surfaces of degree 1

• S. Finashin ^[1] ; V. Kharlamov ^[2]
  1. [1] Middle East Technical University

     Middle East Technical University

     Turquía

     
  2. [2] University of Strasbourg

     University of Strasbourg

     Arrondissement de Strasbourg-Ville, Francia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 5, 2021
• Idioma: inglés
• DOI: 10.1007/s00029-021-00690-x
• Enlaces
  • Texto completo
• Resumen

  • We show how the real lines on a real del Pezzo surface of degree 1 can be split into two species, elliptic and hyperbolic, via a certain distinguished, intrinsically defined, Pin−-structure on the real locus of the surface. We prove that this splitting is invariant under real automorphisms and real deformations of the surface, and that the difference between the total numbers of hyperbolic and elliptic lines is always equal to 16.