Freeness versus maximal global Tjurina number for plane curves
Algebraic Geometry
2017-08-30 v3 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.1508.04954,
title = {Freeness versus maximal global Tjurina number for plane curves},
author = {Alexandru Dimca},
journal= {arXiv preprint arXiv:1508.04954},
year = {2017}
}
Comments
v3: Theorem 1.6 is strengthened and Corollary 1.7 giving a new characterization of nearly free curves is added