Freeness versus maximal global Tjurina number for plane curves

By Alexandru Dimca. Mathematical Proceedings of the Cambridge Philosophical Society, 2015

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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.

Subfields: Algebra and Number Theory, Computational Mechanics, Computational Theory and Mathematics

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