Splitting types of bundles of logarithmic vector fields along plane curves

Takuro Abe, Alexandru Dimca

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10 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

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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