Pencil type line arrangements of low degree: classification and monodromy

• Alexandru Dimca ^[2] ; Denis Ibadula ^[1] ; Daniela Anca Macinic ^[3]
  1. [1] Ovidius University

     Ovidius University

     Rumanía

     
  2. [2] Univ. Nice Sophia Antipolis, France
  3. [3] Simion Stoilow Institute of Mathematics, Bucharest, Romania

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 15, Nº Extra 1 (Special volume), 2016, págs. 249-267
• Idioma: inglés
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  • 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 ≤ 14 lines and having points of multiplicity ≤ 5, we show that the non-triviality of the monodromy on the first cohomology H1(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.