2 problems

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Conjecture on the maximum number of conic-line curves in large degree
Let $P$ be a pencil of degree- $d$ curves, and let $m$ denote the number of conic-line curves in the pencil. Large-degree conic-line pencil conjecture. There does not exist a pencil…
Conjectureopenalgebraic-geometry conic-line-curves pencils-of-curvesarXiv posted 3 days ago
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Uniqueness conjecture for the $(4,d)$ -net Hesse pencil
A $(4,d)$ -net is a configuration associated with a pencil of four degree- $d$ curves whose irreducible components are lines, with the usual net incidence conditions. Hesse pencil un…
Conjectureopenconic-line-curves nets projective-geometryarXiv posted 3 days ago

Conjecture on the maximum number of conic-line curves in large degree