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

4 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
JournalJournal of Algebraic Combinatorics
DOIs
Publication statusAccepted/In press - 2020

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

Fingerprint

Dive into the research topics of 'Addition–deletion results for the minimal degree of logarithmic derivations of hyperplane arrangements and maximal Tjurina line arrangements'. Together they form a unique fingerprint.

Cite this