Saturation of Jacobian ideals: Some applications to nearly free curves,line arrangements and rational cuspidal plane curves期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Saturation of Jacobian ideals: Some applications to nearly free curves,line arrangements and rational cuspidal plane curves

Authors:	Alexandru Dimca Gabriel Sticlaru

Institution:	1. Université Côte d''Azur, CNRS, LJAD and INRIA, France;2. Simion Stoilow Institute of Mathematics, P.O. Box 1-764, RO-014700 Bucharest, Romania;3. Faculty of Mathematics and Informatics, Ovidius University, Bd. Mamaia 124, 900527 Constanta, Romania

Abstract:	In this note we describe the minimal resolution of the ideal $I_{f}$ , the saturation of the Jacobian ideal of a nearly free plane curve $C : f = 0$ . In particular, it follows that this ideal $I_{f}$ can be generated by at most 4 polynomials. Related general results by Hassanzadeh and Simis on the saturation of codimension 2 ideals are discussed in detail. Some applications to rational cuspidal plane curves and to line arrangements are also given.

Keywords:	Corresponding author Primary 14H50 secondary 14B05 13D02 32S22 Jacobian ideal Tjurina number Free curve Nearly free curve Rational cuspidal curve
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