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, vol.23, no.1, pp.123-148, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1017/s1474748022000317
  • Journal Name: Journal of the Institute of Mathematics of Jussieu
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.123-148
  • Keywords: Bertini involution, Enumerative invariants, Pin-structures, Real del Pezzo surfaces, Signed count, Welschinger weight
  • Middle East Technical University Affiliated: Yes

Abstract

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.