On the Number of Conic-Line Curves in a Pencil
MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.23, no.3, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 23 Issue: 3
- Publication Date: 2026
- Doi Number: 10.1007/s00009-026-03125-z
- Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Middle East Technical University Affiliated: Yes
Abstract
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.