TY - JOUR
T1 - Splitting types of bundles of logarithmic vector fields along plane curves
AU - Abe, Takuro
AU - Dimca, Alexandru
N1 - Funding Information:
A part of the argument in the proof of Theorems 5.10 and 5.11 is due to the first author’s joint work with Max Wakefield. The authors are really grateful to him for letting his the argument to be used in this paper. The first author is partially supported by JSPS Grant-in-Aid for Scientific Research (B) 16H03924, and Grant-in-Aid for Exploratory Research 16K13744.
Publisher Copyright:
© 2018 World Scientific Publishing Company.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - 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.
AB - 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.
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U2 - 10.1142/S0129167X18500556
DO - 10.1142/S0129167X18500556
M3 - Article
AN - SCOPUS:85051017819
VL - 29
JO - International Journal of Mathematics
JF - International Journal of Mathematics
SN - 0129-167X
IS - 8
M1 - 1850055
ER -