On the Number of Conic-Line Curves in a Pencil

SULUYER H.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.23, sa.3, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 3
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s00009-026-03125-z
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we study the restrictions on the number m of conic-line curves appearing as special members of pencils of plane curves. Using purely algebraic-geometric and combinatorial arguments, we establish explicit upper bounds on m corresponding to the number p of members of concurrent lines; in particular, we recover the universal bound m <= 6 in these pencils. We further construct a one-parameter family of pencils, such that each pencil in the family contains exactly four conic-line curves. Finally, in the extremal case of a pencil of odd-degree plane curves, we prove that for m = 6, the conic-line members are in general position and determine their irreducible decomposition.