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

Takuro Abe, Alexandru Dimca, Gabriel Sticlaru

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)739-766
Number of pages28
JournalJournal of Algebraic Combinatorics
Volume54
Issue number3
DOIs
Publication statusPublished - Nov 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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