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Article Dans Une Revue Annali della Scuola Normale Superiore di Pisa Année : 2016

Pencil type line arrangements of low degree: classification and monodromy

Alexandru Dimca
Denis Ibadula
  • Fonction : Auteur
Daniela Anca Macinic
  • Fonction : Auteur

Résumé

The complete classification of (3,3)-nets and of (3,4)-nets with only double and triple points is given. Up to lattice isomorphism, there are exactly 3 effective possibilities in each case, and some of these provide new examples of pencil-type line arrangements. For arrangements consisting of at most 14 lines and having points of multiplicity at most 5, we show that the non-triviality of the monodromy on the first cohomology H^1(F) of the associated Milnor fiber F implies the arrangement is of reduced pencil-type. In particular, the monodromy is determined by the combinatorics in such cases.

Dates et versions

hal-00940167 , version 1 (31-01-2014)

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Citer

Alexandru Dimca, Denis Ibadula, Daniela Anca Macinic. Pencil type line arrangements of low degree: classification and monodromy. Annali della Scuola Normale Superiore di Pisa, 2016, XV, pp.249-267. ⟨10.2422/2036-2145.201306_003⟩. ⟨hal-00940167⟩
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