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- Title
Splitting types of bundles of logarithmic vector fields along plane curves.
- Authors
Abe, Takuro; Dimca, Alexandru
- 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 four intersection points.
- Subjects
VECTOR fields; VECTOR bundles; PLANE curves; LOGARITHMIC curves; INVARIANTS (Mathematics); INTERSECTION numbers
- Publication
International Journal of Mathematics, 2018, Vol 29, Issue 8, pN.PAG
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X18500556