COMBINED COUNT of REAL RATIONAL CURVES of CANONICAL DEGREE 2 on REAL DEL PEZZO SURFACES with
Journal of the Institute of Mathematics of Jussieu, vol.23, no.1, pp.123-148, 2024 (SCI-Expanded, Scopus)
- 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.