Pencil type line arrangements of low degree: classification and monodromy
Algebraic Geometry
2013-07-26 v3 Algebraic Topology
Abstract
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.
Keywords
Cite
@article{arxiv.1305.5092,
title = {Pencil type line arrangements of low degree: classification and monodromy},
author = {Alexandru Dimca and Denis Ibadula and Daniela Anca Macinic},
journal= {arXiv preprint arXiv:1305.5092},
year = {2013}
}
Comments
Remark 2.4, (new) Example 2.3 and a couple of references added, typo corrected in Example 2.6 M_1(1) and M_1(2)