On the freeness of Boroczky line arrangements

被引：0
|
作者：
Kabat, Jakub [1 ]
机构：
[1] Inst Matemat UP, Podchorazych 2, PL-30084 Krakow, Poland
来源：
PERIODICA MATHEMATICA HUNGARICA | 2019年 / 78卷 / 01期
关键词：
Line arrangements; Freeness; Hirzebruch inequality; Boroczky arrangements; 52C35; 51D20; 13C10; REAL;
D O I：
10.1007/s10998-018-0250-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present note, we focus on the freeness and some combinatorial properties of line arrangements in the projective plane having only double and triple points. The main result shows that for this class of line arrangements the freeness property is combinatorially determined. As a corollary, we show that Boroczky line arrangements in the sense of Furedi and Palasti (Proc Am Math Soc 92(4):561-566, 1984), except exactly three cases, are not free.
引用
收藏
页码：31 / 37
页数：7
相关论文
共 50 条
  • [21] Conic-Line Arrangements in the Complex Projective Plane
    Piotr Pokora
    Tomasz Szemberg
    Discrete & Computational Geometry, 2023, 69 : 1121 - 1138
  • [22] Conditional probabilities via line arrangements and point configurations
    Clarke, Oliver
    Mohammadi, Fatemeh
    Motwani, Harshit J.
    LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (20): : 5268 - 5300
  • [23] ROOTS OF CHARACTERISTIC POLYNOMIALS AND INTERSECTION POINTS OF LINE ARRANGEMENTS
    Abe, Takuro
    JOURNAL OF SINGULARITIES, 2014, 8 : 100 - 116
  • [24] Unexpected curves arising from special line arrangements
    Michela Di Marca
    Grzegorz Malara
    Alessandro Oneto
    Journal of Algebraic Combinatorics, 2020, 51 : 171 - 194
  • [25] Line and rational curve arrangements, and Walther's inequality
    Dimca A.
    Sticlaru G.
    Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, 2019, 30 (03): : 615 - 633
  • [26] Equidistribution and freeness on Grassmannians
    Browning, Tim
    Horesh, Tal
    Wilsch, Florian
    ALGEBRA & NUMBER THEORY, 2022, 16 (10) : 2385 - 2407
  • [27] Addition-deletion results for the minimal degree of logarithmic derivations of hyperplane arrangements and maximal Tjurina line arrangements
    Abe, Takuro
    Dimca, Alexandru
    Sticlaru, Gabriel
    JOURNAL OF ALGEBRAIC COMBINATORICS, 2021, 54 (03) : 739 - 766
  • [28] Cyclically presented groups, lower central series and line arrangements
    Friedman, Michael
    TOPOLOGY AND ITS APPLICATIONS, 2016, 209 : 239 - 262
  • [29] Multiplier ideals of general line arrangements in C3
    Teitler, Zachariah C.
    COMMUNICATIONS IN ALGEBRA, 2007, 35 (06) : 1902 - 1913
  • [30] The height of a permutation and applications to distance between real line arrangements
    Amram, Meirav
    Cohen, Moshe
    Sun, Hao Max
    Teicher, Mina
    TURKISH JOURNAL OF MATHEMATICS, 2020, 44 (06) : 2041 - 2061
12345