A new bound on the number of special fibers in a pencil of curves

DOI10.1090/S0002-9939-08-09753-0zbMath1173.14021arXiv0801.1521OpenAlexW2067661344MaRDI QIDQ3625537

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Publication date: 5 May 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.1521

zbMATH Keywords

pencil of plane curvesreducible fibers

Mathematics Subject Classification ID

Plane and space curves (14H50) Relations with arrangements of hyperplanes (32S22) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35)

Related Items (16)

3-nets realizing a diassociative loop in a projective plane ⋮ Group-labeled light dual multinets in the projective plane ⋮ Multinets in $$\mathbb{P}^{2}$$ ⋮ \(k\)-nets embedded in a projective plane over a field ⋮ Nets in \(\mathbb{P}^2\) and Alexander duality ⋮ On the structure of 3-nets embedded in a projective plane ⋮ Induced and Complete Multinets ⋮ Equivalence classes of Latin squares and nets in \(\mathbb{CP}^{2}\) ⋮ Hyperplane arrangements and Milnor fibrations ⋮ On line arrangements with applications to 3-nets ⋮ 3-nets realizing a group in a projective plane ⋮ An arithmetic Zariski pair of line arrangements with non-isomorphic fundamental group ⋮ Sigma-invariants and tropical varieties ⋮ FIBERS OF PENCILS OF CURVES ON SMOOTH SURFACES ⋮ On certain extremal pencils of curves with respect to the total reducibility order ⋮ Classification of \(k\)-nets

Cites Work

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• The number of reducible hypersurfaces in a pencil. -- Erratum
• Reducibility of rational functions in several variables
• Completely reducible hypersurfaces in a pencil
• Realization of finite Abelian groups by nets in $\mathbb{P}^2$
• Pencils of Plane Curves and Characteristic Varieties

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