Researcher Database

Faculty of Science Mathematics Mathematics

Researcher Profile and Settings


  • Faculty of Science Mathematics Mathematics

Job Title

  • Professor


  • D. Sc.(Kyoto University)


Research funding number

  • 90467647

J-Global ID

Research Interests

  • topology   combinatorics   algebraic geometry   

Research Areas

  • Natural sciences / Geometry

Academic & Professional Experience

  • 2017/10 - Today Hokkaido University Faculty of Science
  • 2012/04 - 2017/09 Hokkaido University Faculty of Science
  • 2009/04 - 2012/03 Kyoto University Graduate School of Science
  • 2007/09 - 2009/03 Kobe University Graduate School of Science
  • 2006/04 - 2007/08 日本学術振興会海外特別研究員
  • 2004/06 - 2006/03 日本学術振興会特別研究員(PD)
  • 2004/08 - 2004/11 MSRI general member
  • 2004/04 - 2004/05 日本学術振興会特別研究員(DC2)


  • 2002/04 - 2004/05  Kyoto University  Graduate School of Science  Division of Mathematics
  • 2000/04 - 2002/03  Kyoto University  Graduate School of Science  Division of Mathematics
  • 1996/04 - 2000/03  Kyoto University  Faculty of Science

Association Memberships


Research Activities

Published Papers

  • Ahmed Umer Ashraf, Tan Nhat Tran, Masahiko Yoshinaga
    Advances in Applied Mathematics 120 102064 - 102064 0196-8858 2020/09 [Refereed][Not invited]
  • Masahiko Yoshinaga
    European Journal of Mathematics 6 (3) 1097 - 1109 2199-675X 2020/09 [Refereed][Not invited]
  • Kazuki Iijima, Kyouhei Sasaki, Yuuki Takahashi, Masahiko Yoshinaga
    Contributions to Discrete Mathematics 14 (1) 46 - 54 2019/12 [Refereed][Not invited]
  • Ye Liu, Tan Nhat Tran, Masahiko Yoshinaga
    to appear in International Mathematics Research Notices 2019 [Refereed][Not invited]
  • Tan Nhat Tran, Masahiko Yoshinaga
    Journal of Combinatorial Theory, Series A 165 258 - 272 2019 [Refereed][Not invited]
  • Masahiko Yoshinaga
    Journal of Combinatorial Theory. Series A 157 267 - 286 1096-0899 2018/07/01 [Refereed][Not invited]
    The (extended) Linial arrangement LΦ m is a certain finite truncation of the affine Weyl arrangement of a root system Φ with a parameter m. Postnikov and Stanley conjectured that all roots of the characteristic polynomial of LΦ m have the same real part, and this has been proved for the root systems of classical types. In this paper we prove that the conjecture is true for exceptional root systems when the parameter m is sufficiently large. The proof is based on representations of the characteristic quasi-polynomials in terms of Eulerian polynomials.
  • ルート系のLinial配置と特性準多項式
    吉永 正彦
    数理解析研究所講究録 (表現論と組合せ論) 2017 100 - 109 2018/07 [Not refereed][Not invited]
    Tohoku Mathematical Journal 70 39 - 63 2018/03 [Refereed][Not invited]
  • Pauline Bailet, Alexandru Dimca, Masahiko Yoshinaga
    Manuscripta Mathematica 157 (3-4) 1 - 15 0025-2611 2018/01/22 [Refereed][Not invited]
    A general vanishing result for the first cohomology group of affine smooth complex varieties with values in rank one local systems is established. This is applied to the determination of the monodromy action on the first cohomology group of the Milnor fiber of some line arrangements, including the monomial arrangement and the exceptional reflection arrangement of type (Formula presented.).
    Mathematical Research Letters 25 (6) 1977 - 1992 2018 [Refereed][Not invited]
  • Takahiro Hasebe, Toshinori Miyatani, Masahiko Yoshinaga
    Journal of Singularities 16 212 - 227 1949-2006 2017 [Refereed][Not invited]
    The Euler characteristic of a semialgebraic set can be considered as a general- ization of the cardinality of a finite set. An advantage of semialgebraic sets is that we can define “negative sets” to be the sets with negative Euler characteristics. Applying this idea to posets, we introduce the notion of semialgebraic posets. Using “negative posets”, we establish Stanley's reciprocity theorems for order polynomials at the level of Euler characteristics. We also formulate the Euler characteristic reciprocities for chromatic and flow polynomials.
  • Pauline Bailet, Masahiko Yoshinaga
    Journal of Singularities 14 74 - 90 1949-2006 2016/01/01 [Refereed][Not invited]
    We prove vanishing results for the cohomology groups of the Aomoto complex over an arbitrary coefficient ring for real hyperplane arrangements. The proof uses the minimality of arrangements and descriptions of the Aomoto complex in terms of chambers. Our methods are used to present a new proof for the vanishing theorem of local system cohomology groups, a result first proved by Cohen, Dimca, and Orlik.
  • Pauline Bailet, Masahiko Yoshinaga
    GEOMETRIAE DEDICATA 175 (1) 49 - 56 0046-5755 2015/04 [Refereed][Not invited]
    We give a vanishing theorem for the monodromy eigenspaces of the Milnor fibers of complex line arrangements. By applying the modular bound of the local system cohomology groups given by Papadima-Suciu, the result is deduced from the vanishing of the cohomology of certain Aomoto complex over finite fields. In order to prove this, we introduce degeneration homomorphisms of Orlik-Solomon algebras.
  • Masahiko Yoshinaga
    COMBINATORIAL METHODS IN TOPOLOGY AND ALGEBRA 12 143 - 148 2281-518X 2015 [Not refereed][Invited]
    This is a short note on the study of cohomology groups of rank one local systems of real line arrangements via resonant bands. Results on Milnor fibers and several conjectures are also stated.
  • Michele Torielli, Masahiko Yoshinaga
    Journal of Singularities 11 33 - 51 1949-2006 2015/01/01 [Refereed][Not invited]
    The resonant band is a useful notion for the computation of the nontrivial monodromy eigenspaces of the Milnor fiber of a real line arrangement. In this article, we develop the resonant band description for the cohomology of the Aomoto complex. As an application, we prove that real 4-nets do not exist.
  • Shaheen Nazir, Michele Torielli, Masahiko Yoshinaga
    TOPOLOGY AND ITS APPLICATIONS 178 288 - 299 0166-8641 2014/12 [Refereed][Not invited]
    A rank one local system on the complement of a hyperplane arrangement is said to be admissible if it satisfies certain non-positivity condition at every resonant edges. It is known that the cohomology of admissible local system can be computed combinatorially. In this paper, we study the structure of the set of all non-admissible local systems in the character torus. We prove that the set of non-admissible local systems forms a union of subtori. The relations with characteristic varieties are also discussed. (C) 2014 Elsevier B.V. All rights reserved.
  • Masahiko Yoshinaga
    Vietnam Journal of Mathematics 42 (3) 377 - 392 2305-2228 2014/09/01 [Refereed][Not invited]
    We give a new algorithm computing local system cohomology groups for complexified real line arrangements. Using it, we obtain several conditions for the first local system cohomology to vanish and to be at most one-dimensional, which generalize a result by Cohen–Dimca–Orlik. The conditions are described in terms of discrete geometric structures of real figures. The proof is based on a recent study on minimal cell structures. We also compute the characteristic variety of the deleted B3-arrangement.
  • 超平面配置に関する最近の話題
    数学 66 (2) 157 - 179 2014/04 [Refereed][Invited]
  • Freeness of hyperplane arrangements and related topics
    Annales de la Facult\'e des Sciences de Toulouse 23 (2) 483 - 512 2014/03 [Refereed][Invited]
  • Minimal stratification for line arrangements and Milnor fibers
    城崎代数学シンポジウム報告集(2014年10月20日~24日) 114 - 121 2014 [Not refereed][Invited]
  • 共鳴バンド法による局所系係数コホモロジーの計算
    吉永 正彦
    数理解析研究所考究録 1936. 離散群と双曲空間の 複素解析とトポロジー(2014年1月20日~24日) 56 - 67 2014 [Not refereed][Invited]
  • Takuro Abe, Masahiko Yoshinaga
    Mathematische Zeitschrift 275 (3-4) 911 - 919 0025-5874 2013/12 [Refereed][Not invited]
    Ziegler showed that the multirestriction of a free arrangement is also free. After Ziegler's work, several results concerning the "reverse direction", i.e., characterizing freeness of an arrangement via that of its multirestriction, have appeared. In this paper, we prove a new characterization of freeness in which the second Betti number of the arrangement plays a crucial role. © 2013 Springer-Verlag Berlin Heidelberg.
  • Masahiko Yoshinaga
    Journal of Singularities 7 220 - 237 1949-2006 2013 [Refereed][Not invited]
    We study Milnor fibers of complexified real line arrangements. We give a new algorithm computing monodromy eigenspaces of the first cohomology. The algorithm is based on the description of minimal CW-complexes homotopic to the complements, and uses the real figure, that is, the adjacency relations of chambers. It enables us to generalize a vanishing result of Libgober, give new upper-bounds and characterize the A3-arrangement in terms of non-triviality of Milnor monodromy.
  • Ko-Ki Ito, Masahiko Yoshinaga
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 140 (6) 2065 - 2074 0002-9939 2012/06 [Refereed][Not invited]
    We describe an explicit semi-algebraic partition for the complement of a real hyperplane arrangement such that each piece is contractible and so that the pieces form a basis of Borel-Moore homology. We also give an explicit correspondence between the de Rham cohomology and the Borel-Moore homology.
  • Shaheen Nazir, Masahiko Yoshinaga
    ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE 11 (4) 921 - 937 0391-173X 2012 [Refereed][Not invited]
    We prove that, under certain combinatorial conditions, the realization spaces of line arrangements on the complex projective plane are connected. We also give several examples of arrangements with eight, nine and ten lines that have disconnected realization spaces.
  • Masahiko Yoshinaga
    SINGULARITIES IN GEOMETRY AND TOPOLOGY: STRASBOURG 2009 20 345 - 362 2012 [Refereed][Invited]
    The purpose of this paper is applying minimality of hyperplane arrangements to local system cohomology groups. It is well known that twisted cohomology groups with coefficients in a generic rank one local system vanish except in the top degree, and bounded chambers form a basis of the remaining cohomology group. We determine precisely when this phenomenon happens for two-dimensional arrangements.
  • Masahiko Yoshinaga
    ARRANGEMENTS OF HYPERPLANES - SAPPORO 2009 62 523 - 552 2012 [Refereed][Not invited]
    The first part of this paper is a survey on algebro-geometric aspects of sheaves of logarithmic vector fields of hyperplane arrangements. In the second part we prove that the relative de Rham cohomology (of degree two) of ADE-type adjoint quotient map is naturally isomorphic to the module of certain multiderivations. The isomorphism is obtained by the Gauss-Manin derivative of the Kostant-Kirillov form.
  • Masahiko Yoshinaga
    Progress in Mathematics 283 273 - 281 2296-505X 2010 [Refereed][Invited]
    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.
  • Masahiko Yoshinaga
    ARKIV FOR MATEMATIK 47 (2) 393 - 407 0004-2080 2009/10 [Refereed][Not invited]
    We introduce a basis of the Orlik-Solomon algebra labeled by chambers, the 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.
  • Takuro Abe, Masahiko Yoshinaga
    JOURNAL OF ALGEBRA 322 (8) 2839 - 2847 0021-8693 2009/10 [Refereed][Not invited]
    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. (C) 2009 Elsevier Inc. All rights reserved.
  • Kazushi Ueda, Masahiko Yoshinaga
    HOKKAIDO MATHEMATICAL JOURNAL 38 (3) 409 - 415 0385-4035 2009/08 [Refereed][Not invited]
    We show that a smooth divisor-in a projective space can be reconstructed from the isomorphism class of the sheaf of logarithmic vector fields along it if and only if its defining equation is of Sebastiani-Thom type.
  • Takuro Abe, Hiroaki Terao, Masahiko Yoshinaga
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 137 (4) 1405 - 1410 0002-9939 2009 [Refereed][Not invited]
    A central arrangement A of hyperplanes in an l-dimensional vector space V is said to be totally free if a multiarrangement (A, m) is free for any multiplicity m : A -> Z(> 0). It has been known that A is totally free whenever l <= 2. In this article, we will prove that there does not exist any totally free arrangement other than the obvious ones, that is, a product of one-dimensional arrangements and two-dimensional ones.
  • Max Wakefield, Masahiko Yoshinaga
    MATHEMATICAL RESEARCH LETTERS 15 (4) 795 - 799 1073-2780 2008/07 [Refereed][Not invited]
    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.
  • Masahiko Yoshinaga
    TOPOLOGY AND ITS APPLICATIONS 155 (9) 1022 - 1026 0166-8641 2008/04 [Refereed][Not invited]
    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 nontrivial homotopy groups. (C) 2008 Elsevier B.V. All rights reserved.
  • Logarithmic vector fields along smooth plane cubic curves.
    Kumamoto Journal of Mathematics 21 11 - 20 2008/03 [Refereed][Not invited]
  • Minimality of arrangements and applications
    Geometry of Singularities and Manifolds, Kusatsu 2008 11 - 24 2008 [Not refereed][Invited]
  • Takuro Abe, Masahiko Yoshinaga
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 136 (6) 1887 - 1891 0002-9939 2008 [Refereed][Not invited]
    We give a criterion for a reflexive sheaf to split into a direct sum of line bundles.
  • Masahiko Yoshinaga
    KODAI MATHEMATICAL JOURNAL 30 (2) 157 - 194 0386-5991 2007/06 [Refereed][Not invited]
    The Lefschetz hyperplane section theorem asserts that a complex 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 give an explicit description of 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.
  • Masahiko Yoshinaga
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 82 (10) 179 - 182 0386-2194 2006/12 [Refereed][Not invited]
    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.
  • M Yoshinaga
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 37 126 - 134 0024-6093 2005/02 [Refereed][Not invited]
    Hyperplane arrangements in a three-dimensional vector space are considered in this paper. A characterization of the freeness of such an arrangement is given in terms of the characteristic polynomial and a restricted multiarrangement. As an application, the freeness of cones over certain two-dimensional affine arrangements is proved.
  • 超平面配置とLefschetzの超平面切断定理
    吉永 正彦
    数理解析研究所講究録 Recent Topics on Real and Complex Singularities 1501 47 - 60 2005 [Not refereed][Invited]
  • M Yoshinaga
    INVENTIONES MATHEMATICAE 157 (2) 449 - 454 0020-9910 2004/08 [Refereed][Not invited]
    We consider a hyperplane arrangement in a vector space of dimension four or higher. In this case, the freeness of the arrangement is characterized by properties around a fixed hyperplane. As an application, we prove the freeness of cones over certain truncated affine Weyl arrangements which was conjectured by Edelman and Reiner.
  • M Yoshinaga
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 78 (7) 116 - 119 0386-2194 2002/09 [Refereed][Not invited]
    We will prove the freeness of multi-Coxeter arrangements by constructing a basis of the module of vector fields which contact to each reflecting hyperplanes with some multiplicities using K. Saito's theory of primitive derivation.
  • ADE 型随伴商写像の相対ド・ラームコホモロジー
    吉永 正彦
    代数幾何学城崎シンポジウム(2002)報告集 136 - 141 2002 [Not refereed][Invited]

Books etc

  • 周期と実数の$0$-認識問題: Kontsevich-Zagierの予想
    吉永 正彦 (Single work)
    数学書房 2016/02

Conference Activities & Talks

  • A q-deformation of the Aomoto complex  [Invited]
    Masahiko Yoshinaga
    DMV Annual Meeting 2020  2020/09  Zoom (TU Chemnitz)
  • Masahiko Yoshinaga
    Arrangements at Home II (Zoom meeting)  2020/06
  • Icosidodecahedron and Milnor fiber of hyperplane arrangements  [Invited]
    Masahiko Yoshinaga
    第15回代数・解析・幾何学セミナー  2020/02
    Hyperplane arrangements and Japanese Australian workshop on Real and Complex Singularities  2019/12
    Categorical and Analytic Invariants in Algebraic Geometry VII  2019/11
    幾何学コロキウム  2019/10
    Workshop on Hyperplane Arrangements and Reflection Groups  2019/09
  • 吉永 正彦
    離散数学とその応用研究集会2019 (JCCA 2019)  2019/08
    Hyperplane Arrangements in Wakkanai  2019/08
    `New developments in matroid theory'' at the SIAM - Conference on Applied Algebraic Geometry  2019/07
    Magnitude 2019: Analysis, Category Theory, Applications  2019/07
  • On free hyperplane arrangements and Terao’s conjecture. (6 hours lectures)  [Invited]
  • マグニチュードとポセットトポロジー  [Invited]
    吉永 正彦
    数理経済談話会, 信州大学  2019/02
  • Matroids, Tutte polynomial, and generalizations  [Invited]
    Free divisor and hyperplane arrangements  2018/12
  • 平面配置と特性準多項式  [Invited]
    吉永 正彦
    名古屋工業大学談話会  2018/12
  • 組合せ論的相互律とオイラー標数  [Invited]
    吉永 正彦
    東北大学代数幾何セミナー  2018/11
  • G-Tutte polynomials and abelian Lie group arrangements  [Invited]
    The 6th Franco–Japanese–Vietnamese Symposium on Singularites  2018/09
  • Introduction to Catalan arrangements  [Invited]
  • 特性多項式の零点分布からTutte多項式の一般化へ  [Invited]
    吉永 正彦
    北海道大学数学教室談話会  2018/07
  • Tutte polynomials in Geometry and Combinatorics  [Not invited]
    Branched Coverings, Degenerations, and Related Topics 2018  2018/03
  • How many homomorphisms are expected? A motivation for G-Tutte polynomials.  [Not invited]
    A walk between hyperplane arrangements, computer algebra and algorithms.  2018/02
  • 組合せ論的相互律とオイラー標数  [Invited]
    吉永 正彦
    京都大学数学教室大談話会  2017/12
  • 組合せ論的相互律とオイラー標数  [Invited]
    吉永 正彦
    九州大学数理談話会  2017/12
  • A型Catalan配置の対数的ベクトル場の基底  [Invited]
    吉永 正彦
    北海道特殊関数論セミナー  2017/12
  • Catalan配置と原始差分  [Not invited]
    吉永 正彦
    研究集会「不変式・超平面配置と平坦構造」  2017/11
  • ルート系のLinial配置と特性準多項式  [Not invited]
    吉永 正彦
    表現論と組合せ論  2017/10
  • G-Tutte polynomials  [Invited]
    Matroids over Hyperfields  2017/08
  • G-Tutte polynomials  [Not invited]
    Advances in Hyperplane Arrangements  2017/08
  • Remarks on characteristic quasi-polynomials of deformed Weyl arrangements  [Invited]
    Mathematical Congress of the Americas 2017, Session ``Advances in Arrangement Theory''  2017/07
  • G-Tutte polynomials  [Invited]
    Encounter in Topology 'n Algebra (ET'nA 2017)  2017/06
  • Characteristic polynomials of Linial arrangements.  [Invited]
    Oberseminar Lie Theorie  2017/05
  • Characteristic polynomials of Linial arrangements  [Invited]
    Mathematics and String Theory Seminar, Kavli IPMU  2017/02
  • Around the h-shift problem  [Not invited]
    Hyperplane Arrangements and related topics  2017/02
  • Characteristic polynomials of hyperplane arrangements  [Invited]
    Colloquium, Fribourg University  2016/11
  • The Euler characteristic reciprocity for order polynomials  [Invited]
    The 4th Franco-Japanese-Vietnamese Singularities  2016/11
  • What makes roots lying on a line?  [Invited]
    Combinatorial Structures in Algebra, Geometry and Topology.  2016/10
  • The Euler characteristic reciprocity for order polynomials  [Invited]
    Enumerative, algebraic and geometric aspects of arrangements, Bremen University  2016/08
  • Hyperplane arrangements and the Eulerian polynomial  [Invited]
    Summer Conference on Hyperplane Arrangements(SCHA) in Sapporo  2016/08
  • Euler characteristics in enumerative combinatorics  [Invited]
    Asian Mathematical Conference (AMC 2016), Bali  2016/07

Awards & Honors

  • 2017/04 文部科学省 平成29年度文部科学大臣表彰若手科学者賞
    受賞者: 吉永 正彦

Educational Activities

Teaching Experience

  • Special lecture on Geometry
    開講年度 : 2018
    課程区分 : 修士課程
    開講学部 : 理学院
    キーワード : Hyperplane arrangements, Grobner basis, CoCoA.
  • Inter-Graduate School Classes(General Subject):Natural and Applied Sciences
    開講年度 : 2018
    課程区分 : 修士課程
    開講学部 : 大学院共通科目
  • Geometry C
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 基本群、被覆空間
  • Linear Algebra I
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 行列, 連立1次方程式, 基本変形, 階数, 行列式, 逆行列

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