29 research outputs found
Addition-Deletion Theorems for Factorizations of Orlik-Solomon Algebras and nice Arrangements
We study the notion of a nice partition or factorization of a hyperplane
arrangement due to Terao from the early 1990s. The principal aim of this note
is an analogue of Terao's celebrated addition-deletion theorem for free
arrangements for the class of nice arrangements. This is a natural setting for
the stronger property of an inductive factorization of a hyperplane arrangement
by Jambu and Paris.
In addition, we show that supersolvable arrangements are inductively factored
and that inductively factored arrangements are inductively free. Combined with
our addition-deletion theorem this leads to the concept of an induction table
for inductive factorizations.
Finally, we prove that the notions of factored and inductively factored
arrangements are compatible with the product construction for arrangements.Comment: 24 pages; v2 26 pages: added new example over complex numbers of an
inductively free and factored arrangement which is not inductively factored,
added comment on proper containment of hereditary factored classes; v3 final
version, small changes as suggested by referees; to appear in European. J.
Com
On inductively free Restrictions of Reflection Arrangements
Let W be a finite complex reflection group acting on the complex vector space
V and let A(W) = (A(W), V) be the associated reflection arrangement. In an
earlier paper by the last two authros, we classified all inductively free
reflection arrangements A(W). The aim of this note is to extend this work by
determining all inductively free restrictions of reflection arrangements.Comment: 15 pages, final version to appear in Journal of Algebr