
TL;DR
This paper investigates the maximum number of conic-line curves in special pencils, establishing bounds related to concurrent lines, and constructs examples with exactly four conic-line curves, including general position cases.
Contribution
It provides new bounds on the number of conic-line curves in pencils and constructs explicit families with a fixed number of such curves.
Findings
Upper bounds on conic-line curves related to concurrent lines
Construction of pencils with exactly four conic-line curves
Analysis of conic-line curves in general position
Abstract
In this paper, we study the restrictions on the number of conic-line curves in special pencils. The most general result we obtain is the relation between upper bounds on and the number of concurrent lines in these pencils. We construct a one-parameter family of pencils such that each pencil in the family contains exactly 4 conic-line curves. We also deal with pencils whose conic-line curves are in general position.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques
