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

Finashin S., Kharlamov V.

SELECTA MATHEMATICA-NEW SERIES, cilt.27, sa.5, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 5
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s00029-021-00690-x
  • Dergi Adı: SELECTA MATHEMATICA-NEW SERIES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: Real del Pezzo surfaces, Enumerative invariants, Counting real lines, Pin-structures, Elliptic and hyperbolic lines
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.