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山东大学学报（理学版） ›› 2014, Vol. 49 ›› Issue (12): 66-70.doi: 10.6040/j.issn.1671-9352.0.2014.187

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G2型Shi-Catalan构形的自由性

高瑞梅   

  1. 长春理工大学理学院, 吉林 长春 130022
  • 收稿日期:2014-04-28 修回日期:2014-09-09 出版日期:2014-12-20 发布日期:2014-12-20
  • 作者简介:高瑞梅(1983- ),女,博士,讲师,研究方向为奇点理论和超平面构形. E-mail:gaorm135@nenu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11271063, 11326078); 黑龙江省教育厅科技研究项目(12531187)

The freeness of Shi-Catalan arrangements of type G2

GAO Rui-mei   

  1. Department of Science, Changchun University of Science and Technology, Changchun 130022, Jilin, China
  • Received:2014-04-28 Revised:2014-09-09 Online:2014-12-20 Published:2014-12-20

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摘要： G2型Shi-Catalan构形是二维空间中的重构形, 它是将G2型Weyl构形在同一轨道中的超平面赋予相同的重数而得到的构形。 给出了G2型Shi-Catalan构形的4种具体形式, 通过将构形投影到射影平面计算构形中超平面交点个数的方法, 证明了G2型Shi-Catalan构形的锥构形都是自由的。

关键词: Shi-Catalan构形, 自由性, Weyl构形

Abstract: The Shi-Catalan arrangements of type G2 are multiarrangements in the 2-dimensional vector space, which are obtained by giving the same multiplicity to the hyperplanes in the same orbit in Weyl arrangements of type G2. Four concrete forms of Shi-Catalan arrangements of type G2 are given. By counting the intersections of hyperplanes in reflection planes, we prove the conclusion that the cones over the Shi-Catalan arrangements of type G2 are all free.

Key words: Weyl arrangement, freeness, Shi-Catalan arrangement

中图分类号: 

  • O189
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[1] 高瑞梅,初颖. Weyl构形An-1和Bn之间的构形的自由性[J]. 山东大学学报（理学版）, 2018, 53(6): 70-75.
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