We introduce a new class of arrangements of hyperplanes, called (strictly) plus-one
generated arrangements, from algebraic point of view. Plus-one generatedness is close to …

Abstract Let (A, A', A^ H)(A, A′, AH) be the triple of hyperplane arrangements. We show that
the freeness of A^ H AH and the division of χ (A\,;\, t) χ (A; t) by χ (A^ H\,; t) χ (AH; t) imply the …

Abstract Let C=∪ ni= 1 Ci⊆ ℙ2 be a collection of smooth rational plane curves. We prove
that the addition–deletion operation used in the study of hyperplane arrangements has an …

Conjectures of Suciu “Fundamental groups of line arrangements: Enumerative aspects,” 43–
79. Contemporary Mathematics 276. Providence, RI: American Mathematical Society, 2001 …

Building on work of Brandt and Terao in their study of k-formality, we introduce a co-chain
complex associated to a multi-arrangement and prove that its cohomologies determine …

This paper provides an overview of selected results and open problems in the theory of
hyperplane arrangements, with an emphasis on computations and examples. We give an …

We show that the deletion theorem of a free arrangement is combinatorial, ie, whether we
can delete a hyperplane from a free arrangement keeping freeness depends only on the …

We consider the behaviour of logarithmic differential forms on arrangements and
multiarrangements of hyperplanes under the operations of deletion and restriction …

We define specific multiplicities on the braid arrangement by using signed graphs. To
consider their freeness, we introduce the notion of signed-eliminable graphs as a …

We define a chain complex for generalized splines on graphs, analogous to that introduced
by Billera and refined by Schenck–Stillman for splines on polyhedral complexes. The …