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On rational cuspidal plane curves, and the local cohomology of Jacobian rings

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arxiv 1707.05258 v4 pith:KHAXYUKW submitted 2017-07-17 math.AG math.AC

Alexandru Dimca This is my paper · ORCID
classification math.AGmath.AC
keywords curvescuspidalfreeplanerationalarrangementcharacterizationsclassification
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This note gives the complete projective classification of rational, cuspidal plane curves of degree at least 6, and having only weighted homogeneous singularities. It also sheds new light on some previous characterizations of free and nearly free curves in terms of Tjurina numbers. Finally, we suggest a stronger form of Terao's conjecture on the freeness of a line arrangement being determined by its combinatorics.

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  1. Addition-deletion results for the minimal degree of logarithmic derivations of arrangements

    math.AG 2019-08 conditional novelty 7.0 of 10

    For line arrangements, the minimal degree of a logarithmic derivation changes predictably under adding or deleting one line, yielding new maximal Tjurina arrangements and a sharp n3≤5 combinatoriality threshold.

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