On the splitting types of bundles of logarithmic vector fields along plane curves

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.

References in corpus (1)

• Nearly free divisors and rational cuspidal curves

Cited by in corpus (4)

• Nearly free curves and arrangements: a vector bundle point of view
• Plane curves with three syzygies, minimal Tjurina curves curves, and nearly cuspidal curves
• Projective dimensions of hyperplane arrangements
• Saturation of Jacobian ideals: some applications to nearly free curves, line arrangements and rational cuspidal plane curves