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Masahiko Yoshinaga

Publications and source records attributed to Masahiko Yoshinaga.

66 records · Page 4Linked to original sources
arXiv2008

On the extendability of free multiarrangements

A free multiarrangement of rank $k$ is defined to be extendable if it is obtained from a simple rank $(k+1)$ free arrangement by the natural restriction to a hyperplane (in the sense of Ziegler). Not all free multiarrangements are extendable. We will discuss extendability of free multiarrangements for a special class. We also give two applications. The first is to produce totally non-free arrangements. The second is to give interpolating free arrangements between extended Shi and Catalan arrangements.

math.CO↗
arXiv2007

Generic section of a hyperplane arrangement and twisted Hurewicz maps

We consider a twisted version of the Hurewicz map on the complement of a hyperplane arrangement. The purpose of this paper is to prove surjectivity of the twisted Hurewicz map under some genericity conditions. As a corollary, we also prove that a generic section of the complement of a hyperplane arrangement has non-trivial homotopy groups.

math.GT↗
arXiv2007

Coxeter multiarrangements with quasi-constant multiplicities

We study structures of derivation modules of Coxeter multiarrangements with quasi-constant multiplicities by using the primitive derivation. As an application, we show that the characteristic polynomial of a Coxeter multiarrangement with quasi-constant multiplicity is combinatorially computable.

math.CO↗
arXiv2007

The Jacobian ideal of a hyperplane arrangement

The Jacobian ideal of a hyperplane arrangement is an ideal in the polynomial ring whose generators are the partial derivatives of the arrangements defining polynomial. In this article, we prove that an arrangement can be reconstructed from its Jacobian ideal.

math.AC↗
arXiv2007

Chamber basis of the Orlik-Solomon algebra and Aomoto complex

We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.

math.GT↗
arXiv2007

Hyperplane arrangements and Lefschetz's hyperplane section theorem

The Lefschetz hyperplane section theorem asserts that an affine variety is homotopy equivalent to a space obtained from its generic hyperplane section by attaching some cells. The purpose of this paper is to describe attaching maps of these cells for the complement of a complex hyperplane arrangement defined over real numbers. The cells and attaching maps are described in combinatorial terms of chambers. We also discuss the cellular chain complex with coefficients in a local system and a presentation for the fundamental group associated to the minimal CW-decomposition for the complement.

math.AG↗
arXiv2006

Free Arrangements over Finite Field

The freeness of hyperplane arrangements in a three dimensional vector space over finite field is discussed. We prove that if the number of hyperplanes is greater than some bound, then the freeness is determined by the characteristic polynomial.

math.CO↗
arXiv2005

Splitting criterion for reflexive sheaves

The purpose of this paper is to study the structure of reflexive sheaves over projective spaces through hyperplane sections. We give a criterion for a reflexive sheaf to split into a direct sum of line bundles. An application to the theory of free hyperplane arrangements is also given.

math.AG↗
arXiv2004

Some characterizations of freeness of hyperplane arrangement

We will consider some characterizations of freeness of a hyperplane arrangement, in terms of the following properties: locally freeness, factorization of characteristic polynomial and freeness of restricted multiarrangement. In the case of 3-arrangement, freeness is characterized by factorization of characteristic polynomial and coincidence of its roots with exponents of restricted multiarrangement. In the case of higher dimension, it is characterized by a kind of locally freeness and freeness of restricted multiarrangement. As an application, we prove the freeness of certain arrangements which is conjectured by Edelman and Reiner.

math.CO↗