Freeness versus maximal global Tjurina number for plane curves

Abstract

We give a characterization of nearly free plane curves in terms of their global Tjurina numbers, similar to the characterization of free curves as curves with a maximal Tjurina number, due to 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 characterization of free curves and a simple characterization of nearly free curves in terms of their syzygies conclude this note.

v3: Theorem 1.6 is strengthened and Corollary 1.7 giving a new characterization of nearly free curves is added

References in corpus (4)

• Nearly free divisors and rational cuspidal curves
• Syzygies of Jacobian ideals and defects of linear systems
• Free and nearly free surfaces in $P^3$
• Elementary modifications and line configurations in P^2

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• Plane curves with three syzygies, minimal Tjurina curves curves, and nearly cuspidal curves
• Jacobian syzygies and plane curves with maximal global Tjurina numbers
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• On combinatorial bounds for the total Tjurina numbers of certain curves and surfaces with isolated singularities
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