Splitting types of bundles of logarithmic vector fields along plane curves

Takuro Abe, Alexandru Dimca

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.

Original languageEnglish
Article number1850055
JournalInternational Journal of Mathematics
Volume29
Issue number8
DOIs
Publication statusPublished - Jul 1 2018

Fingerprint

Plane Curve
Arrangement
Bundle
Vector Field
Logarithmic
Line
Intersection
Curve
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Splitting types of bundles of logarithmic vector fields along plane curves. / Abe, Takuro; Dimca, Alexandru.

In: International Journal of Mathematics, Vol. 29, No. 8, 1850055, 01.07.2018.

Research output: Contribution to journalArticle

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