Addition–deletion results for the minimal degree of logarithmic derivations of hyperplane arrangements and maximal Tjurina line arrangements

Takuro Abe, Alexandru Dimca, Gabriel Sticlaru

研究成果: Contribution to journalArticle査読

4 被引用数 (Scopus)

抄録

We study the change of the minimal degree of a logarithmic derivation of a hyperplane arrangement under the addition or the deletion of a hyperplane and give a number of applications. First, we prove the existence of Tjurina maximal line arrangements in a lot of new situations. Then, starting with Ziegler’s example of a pair of arrangements of d= 9 lines with n3= 6 triple points in addition to some double points, having the same combinatorics, but distinct minimal degree of a logarithmic derivation, we construct new examples of such pairs, for any number d≥ 9 of lines, and any number n3≥ 6 of triple points. Moreover, we show that such examples are not possible for line arrangements having only double and triple points, with n3≤ 5.

本文言語英語
ジャーナルJournal of Algebraic Combinatorics
DOI
出版ステータス受理済み/印刷中 - 2020

All Science Journal Classification (ASJC) codes

  • 代数と数論
  • 離散数学と組合せ数学

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