Arrangements of hyperplanes and conics via real structures

• Project/Area Number: 25400060
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Hokkaido University
• Principal Investigator: YOSHINAGA Masahiko 北海道大学, 理学(系)研究科(研究院), 准教授 (90467647)
• Co-Investigator(Kenkyū-buntansha): TERAO Hiroaki 北海道大学, 国際本部, 特任教授 (90119058)
• Co-Investigator(Renkei-kenkyūsha): TOKUNAGA Hiro-o 首都大学東京, 大学院理工学研究科, 教授 (30211395)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 超平面配置 / ミルナーファイバー / オイラー多項式 / 実構造 / 二次曲線配置 / 特性多項式 / エルハルト多項式

Outline of Final Research Achievements

We studied topological and combinatorial aspects of hyperplane arrangements. As topological aspects, we focused on Milnor fibers of hyperplane arrangements. Based on the formula describing the cohomology of Milnor fiber using real structure, we obtained certain vanishing of non-trivial monodromy.
We also studied the characteristic quasi-polynomials of Linial arrangements associated to a root system in terms of Ehrhart theory.

Research Products

• [Int'l Joint Research] Nice大学(フランス)
• [Journal Article] Degeneration of Orlik-Solomon algebras and Milnor fibers of complex line arrangements (2016)
  • Author(s): Pauline Bailet, Masahiko Yoshinaga
  • Journal Title: Geometriae Dedicata Volume: 未定 Issue: 1 Pages: 49-56
  • DOI: 10.1007/s10711-014-0027-7
  • Peer Reviewed
• [Journal Article] Resonant bands, Aomoto complex, and real 4-nets (2015)
  • Author(s): Michele Torielli, Masahiko Yoshinaga
  • Journal Title: Journal of Singularities Volume: 11 Pages: 33-51
  • DOI: 10.5427/jsing.2015.11b
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Free arrangements and coefficients of characteristic polynomials (2013)
  • Author(s): Takuro Abe and Masahiko Yoshinaga
  • Journal Title: Mathematische Zeitschrift Volume: 275 Issue: 3-4 Pages: 911-919
  • DOI: 10.1007/s00209-013-1165-6
  • Peer Reviewed
• [Journal Article] Milnor fibers of real line arrangements (2013)
  • Author(s): M.Yoshinaga
  • Journal Title: Journal of Singularities Volume: 7 Pages: 220-237
  • DOI: 10.5427/jsing.2013.7l
  • Peer Reviewed
• [Presentation] Linial arrangements and Eulerian polynomials (2016)
  • Author(s): Masahiko Yoshinaga
  • Organizer: Special Session on Topology and Combinatorics of Arrangements (in honor of Mike Falk), Spring Eastern Sectional Meeting State University of New York at Stony Brook
  • Place of Presentation: NY (USA)
  • Year and Date: 2016-03-19
  • Int'l Joint Research / Invited
• [Presentation] Euler characteristics in enumerative combinatorics (2016)
  • Author(s): Masahiko Yoshinaga
  • Organizer: Colloquium, Universite de Bourgogne
  • Place of Presentation: Bourgogne大学(Dijon, France)
  • Year and Date: 2016-03-10
  • Int'l Joint Research / Invited
• [Presentation] Euler characteristic reciprocity for chromatic and order polynomials (2016)
  • Author(s): Masahiko Yoshinaga
  • Organizer: SINGULARITIES AND TOPOLOGY
  • Place of Presentation: Nice大学(Nice, France)
  • Year and Date: 2016-03-08
  • Int'l Joint Research / Invited
• [Presentation] Functorizations of enumerative problems (2016)
  • Author(s): Masahiko Yoshinaga
  • Organizer: Hokkaido University - KAIST (ASARC) Joint Workshop Algebra and Geometry
  • Place of Presentation: 北海道大学(北海道・札幌市)
  • Year and Date: 2016-01-06
  • Int'l Joint Research / Invited
• [Presentation] Hyperplane arrangements and Eulerian polynomials (2015)
  • Author(s): Masahiko Yoshinaga
  • Organizer: Computational Geometric Topology in Arrangement Theory
  • Place of Presentation: ICERM, Providence (USA)
  • Year and Date: 2015-07-09
  • Int'l Joint Research / Invited
• [Presentation] 超平面配置とオイラー多項式 (2015)
  • Author(s): 吉永正彦
  • Organizer: 幾何学・組合せ論に現れる環と代数構造
  • Place of Presentation: 京都大学数理解析研究所（京都府・京都市）
  • Year and Date: 2015-06-11
  • Invited
• [Presentation] 超平面配置とオイラー多項式 (2015)
  • Author(s): 吉永正彦
  • Organizer: 代数セミナー
  • Place of Presentation: 広島大学（広島県・東広島市）
  • Year and Date: 2015-06-05
  • Invited
• [Presentation] 超平面配置の特性多項式 (2015)
  • Author(s): 吉永正彦
  • Organizer: 広島大学談話会
  • Place of Presentation: 広島大学（広島県・東広島市）
  • Year and Date: 2015-06-02
  • Invited
• [Presentation] Milnor fibers of real line arrangements (2015)
  • Author(s): Masahiko Yoshinaga
  • Organizer: Arrangements of plane curves and related problems
  • Place of Presentation: 首都大学東京（東京都八王子市）
  • Year and Date: 2015-03-18
  • Invited
• [Presentation] Worpitzky partition, Eulerian polynomial and Linial arrangements (2015)
  • Author(s): Masahiko Yoshinaga
  • Organizer: Perspectives in Lie Theory
  • Place of Presentation: Scuola Normale Superiore （イタリア）
  • Year and Date: 2015-02-12
  • Invited
• [Presentation] Minimal stratification for line arrangements and Milnor fibers (2014)
  • Author(s): Masahiko Yoshinaga
  • Organizer: 城崎代数幾何シンポジウム
  • Place of Presentation: 城崎アートセンター（兵庫県豊岡市）
  • Year and Date: 2014-10-24
  • Invited
• [Presentation] Milnor fibers and semi-algebraic stratifications of real line arrangements (2014)
  • Author(s): Masahiko Yoshinaga
  • Organizer: 代数幾何セミナー
  • Place of Presentation: 東北大学（仙台市）
  • Year and Date: 2014-07-11
  • Invited
• [Presentation] Milnor fibers and semi-algebraic stratifications of real line arrangements (2014)
  • Author(s): Masahiko Yoshinaga
  • Organizer: Geometry Conference - Mathematics New Goals
  • Place of Presentation: National Cheng Kung University（台湾）
  • Year and Date: 2014-06-30 – 2014-07-04
  • Invited
• [Presentation] Resonant bands, Aomoto complex, and Real 4-nets (2014)
  • Author(s): Masahiko Yoshinaga
  • Organizer: Topology of arrangement of hyperplanes and hypersurface singularity
  • Place of Presentation: 東京理科大学（東京都新宿区）
  • Year and Date: 2014-04-26
  • Invited
• [Presentation] Milnor fibers of real line arrangements (2014)
  • Author(s): Masahiko Yoshinaga
  • Organizer: 離散群と双曲空間の複素解析とトポロジー
  • Place of Presentation: 京都大学数理解析研究所（京都市）
• [Presentation] Milnor fibers of real line arrangements (2014)
  • Author(s): Masahiko Yoshinaga
  • Organizer: NEW PERSPECTIVES IN HYPERPLANE AND REFLECTION ARRANGEMENTS
  • Place of Presentation: Bochum 大学（ドイツ）
• [Presentation] 実直線配置のミルナーファイバー (2013)
  • Author(s): 吉永正彦
  • Organizer: 代数学セミナー
  • Place of Presentation: 広島大学（東広島市）
• [Presentation] Milnor fibers of real line arrangements (2013)
  • Author(s): Masahiko Yoshinaga
  • Organizer: The 2nd Pacific RIM Mathematical Association Congress
  • Place of Presentation: 上海交通大学（中国）
• [Presentation] Milnor fibers of real line arrangements (2013)
  • Author(s): Masahiko Yoshinaga
  • Organizer: The 6th Pacific RIM Conference on Mathematics 2013
  • Place of Presentation: Sapporo Convention Center（北海道）
• [Presentation] Milnor fibers of real line arrangements (2013)
  • Author(s): Masahiko Yoshinaga
  • Organizer: Combinatorial Methods in Topology and Algebra
  • Place of Presentation: Cortona（イタリア）
• [Presentation] Milnor fibers of real line arrangements (2013)
  • Author(s): Masahiko Yoshinaga
  • Organizer: The 1st Franco-Japanese-Vietnamese Symposium on Singularities
  • Place of Presentation: Nice 大学（フランス）
• [Book] 周期と実数の0-認識問題: Kontsevich-Zagierの予想 (2016)
  • Author(s): 吉永正彦
  • Total Pages: 193
  • Publisher: 数学書房
• [Remarks]
  • URL: http://www.math.sci.hokudai.ac.jp/~yoshinaga/jindex.html
• [Remarks] Masahiko Yoshinaga
  • URL: http://www.math.sci.hokudai.ac.jp/~yoshinaga/index.html