The real Mordell-Weil group of rational elliptic surfaces and real lines on del Pezzo surfaces of degree <i>K<SUP>2</SUP></i>=1

FİNASHİN S., Kharlamov V.

REVISTA MATEMATICA COMPLUTENSE, cilt.39, sa.3, ss.635-694, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 3
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s13163-025-00553-5
  • Dergi Adı: REVISTA MATEMATICA COMPLUTENSE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
  • Sayfa Sayıları: ss.635-694
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We undertake a study of topological properties of the real Mordell-Weil group MWR of real rational elliptic surfaces X which we accompany by a related study of real lines on X and on the "subordinate" del Pezzo surfaces Y of degree 1. We give an explicit description of isotopy types of real lines on Y-R and an explicit presentation of MWR in the mapping class group Mod(X-R). Combining these results we establish an explicit formula for the action of MWR in H-1(X-R).