Deletion theorem and combinatorics of hyperplane arrangements

Research output: Contribution to journalArticle

Abstract

We show that the deletion theorem of a free arrangement is combinatorial, i.e., whether we can delete a hyperplane from a free arrangement keeping freeness depends only on the intersection lattice. In fact, we give a sufficient and necessary condition for the deletion theorem in terms of characteristic polynomials. As a corollary, we prove that whether a free arrangement has a free filtration is also combinatorial. The proof is based on the result about a minimal set of generators of a logarithmic derivation module of a multiarrangement which satisfies the b 2 -equality.

Original languageEnglish
Pages (from-to)581-595
Number of pages15
JournalMathematische Annalen
Volume373
Issue number1-2
DOIs
Publication statusPublished - Feb 8 2019

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Arrangement of Hyperplanes
Combinatorics
Deletion
Arrangement
Theorem
Minimal Set
Characteristic polynomial
Hyperplane
Filtration
Corollary
Logarithmic
Equality
Intersection
Generator
Necessary Conditions
Module
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Deletion theorem and combinatorics of hyperplane arrangements. / Abe, Takuro.

In: Mathematische Annalen, Vol. 373, No. 1-2, 08.02.2019, p. 581-595.

Research output: Contribution to journalArticle

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