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Freeness versus maximal global Tjurina number for plane curves

Published online by Cambridge University Press:  21 September 2016

ALEXANDRU DIMCA
ALEXANDRU DIMCA*
Affiliation:
Université Côte d'Azur, CNRS, LJAD, France. e-mail: dimca@unice.fr
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Abstract

We give a characterisation of nearly free plane curves in terms of their global Tjurina numbers, similar to the characterisation of free curves as curves with a maximal Tjurina number, given by A. A. du Plessis and C.T.C. Wall. It is also shown that an irreducible plane curve having a 1-dimensional symmetry is nearly free. A new numerical characterisation of free curves and a simple characterisation of nearly free curves in terms of their syzygies conclude this paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 163 , Issue 1 , July 2017 , pp. 161 - 172
Copyright
Copyright © Cambridge Philosophical Society 2016 

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References

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