Rumanía
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.
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