On the splitting types of bundles of logarithmic vector fields along plane curves
Algebraic Geometry
2019-09-17 v1 Combinatorics
Abstract
We give a formula relating the total Tjurina number and the generic splitting type of the bundle of logarithmic vector fields associated to a reduced plane curve. By using it, we give a characterization of nearly free curves in terms of splitting types. Several applications to free and nearly free arrangements of lines are also given, in particular a proof of a form of Terao's Conjecture for arrangements having a line with at most 4 intersection points.
Cite
@article{arxiv.1706.05146,
title = {On the splitting types of bundles of logarithmic vector fields along plane curves},
author = {Takuro Abe and Alexandru Dimca},
journal= {arXiv preprint arXiv:1706.05146},
year = {2019}
}