Line and rational curve arrangements, and Walther's inequality

被引：0
作者：
Dimca A. [1 ]
Sticlaru G. [2 ]
机构：
[1] Université Cote d'Azur, CNRS, LJAD
[2] Faculty of Mathematics and Informatics, Ovidius University, Bd. Mamaia 124, Constanta
来源：
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni | 2019年 / 30卷 / 03期
关键词：
Free curve; Freeness defect; Line arrangements; Spectrum; Tjurina number;
D O I：
10.4171/RLM/862
中图分类号：
学科分类号：
摘要：
There are two invariants associated to any line arrangement: The freeness defect n(C) and an upper bound for it, denoted by n0(C), coming from a recent result by Uli Walther. We show that n0(C) is combinatorially determined, at least when the number of lines in C is odd, while the same property is conjectural for n(C). In addition, we conjecture that the equality n(C) = n0(C) holds if and only if the essential arrangement C of d lines has either a point of multiplicity d -1, or has only double and triple points. We prove both conjectures in some cases, in particular when the number of lines is at most 10. We also extend a result by H. Schenck on the Castenuovo-Mumford regularity of line arrangements to arrangements of possibly singular rational curves. © 2019 European Mathematical Society Publishing House. All rights reserved.
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页码：615 / 633
页数：18
相关论文
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