COMBINED COUNT of REAL RATIONAL CURVES of CANONICAL DEGREE 2 on REAL DEL PEZZO SURFACES with

FİNASHİN S., Kharlamov V.

Journal of the Institute of Mathematics of Jussieu, cilt.23, sa.1, ss.123-148, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1017/s1474748022000317
  • Dergi Adı: Journal of the Institute of Mathematics of Jussieu
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.123-148
  • Anahtar Kelimeler: Bertini involution, Enumerative invariants, Pin-structures, Real del Pezzo surfaces, Signed count, Welschinger weight
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We propose two systems of intrinsic weights for counting such curves. In both cases the result acquires an exceptionally strong invariance property: it does not depend on the choice of a surface. One of our counts includes all divisor classes of canonical degree 2 and gives in total 30. The other one excludes the class, but adds up the results of counting for a pair of real structures that differ by Bertini involution. This count gives 96.