A description of the resonance variety of a line combinatorics via combinatorial pencils

DOI10.1007/s00373-009-0863-7zbMath1230.14080OpenAlexW1985194845MaRDI QIDQ844228

Miguel Ángel Marco Buzunáriz

Publication date: 18 January 2010

Published in: Graphs and Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00373-009-0863-7

zbMATH Keywords

line arrangementpencilresonance variety

Mathematics Subject Classification ID

Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Projective techniques in algebraic geometry (14N05) Pencils, nets, webs in algebraic geometry (14C21)

Related Items (14)

3-nets realizing a diassociative loop in a projective plane ⋮ The loop-linking number of line arrangements ⋮ Group-labeled light dual multinets in the projective plane ⋮ An equivariant discrete model for complexified arrangement complements ⋮ \(k\)-nets embedded in a projective plane over a field ⋮ Around the Tangent Cone Theorem ⋮ Discriminantal bundles, arrangement groups, and subdirect products of free groups ⋮ Isotropic subspaces of Orlik-Solomon algebras ⋮ Modular equalities for complex reflection arrangements ⋮ 3-nets realizing a group in a projective plane ⋮ An arithmetic Zariski pair of line arrangements with non-isomorphic fundamental group ⋮ Depth of cohomology support loci for quasi-projective varieties via orbifold pencils ⋮ Classification of \(k\)-nets ⋮ Complements to Ample Divisors and Singularities

Uses Software

• GAP

Cites Work

• Characteristic varieties and constructible sheaves
• Combinatorics and topology of complements of hyperplanes
• Arrangements and cohomology
• The braid monodromy of plane algebraic curves and hyperplane arrangements
• Topology and combinatorics of real line arrangements
• On the holonomy Lie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces
• Realization of finite Abelian groups by nets in $\mathbb{P}^2$
• Combinatorial and algebraic structure in Orlik-Solomon algebras
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