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


Finashin S., Kharlamov V.

SELECTA MATHEMATICA-NEW SERIES, vol.27, no.5, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.1007/s00029-021-00690-x
  • Journal Name: SELECTA MATHEMATICA-NEW SERIES
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Keywords: Real del Pezzo surfaces, Enumerative invariants, Counting real lines, Pin-structures, Elliptic and hyperbolic lines

Abstract

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.