Research on subrings and automorphisms of a polynomial ring

• Project/Area Number: 19840041
• Research Category: Grant-in-Aid for Young Scientists (Start-up)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: KURODA Shigeru Tokyo Metropolitan University, 大学院・理工学研究科, 准教授 (70453032)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,983,000 (Direct Cost: ¥2,590,000、Indirect Cost: ¥393,000); Fiscal Year 2008: ¥1,703,000 (Direct Cost: ¥1,310,000、Indirect Cost: ¥393,000); Fiscal Year 2007: ¥1,280,000 (Direct Cost: ¥1,280,000)
• Keywords: アフィン代数幾何学 / 多項式環論 / 多項式環 / 自己同型群 / 正標数 / 微分作用素 / イニシャル代数 / 高次微分 / Shestakov・Umirbaev理論 / Shestakov-Umirbaev理論 / ヒルベルトの第14問題 / 部分環 / Tame Generators Problem

Research Abstract

多項式環に関して基本的な対象である部分環と自己同型を中心に研究し、部分環の有限生成性に関するヒルベルトの第14問題や、自己同型群の生成に関するTame Generators Problemなどにおいて、いくつかの新しい結果を得た。特に、自己同型群の研究では、最近、歴史的難問を解決したShestakovとUmirbaevの理論を、部分環の解析のために我々が独自に培った技術を応用して再構築した。それにより、多項式環の自己同型群の構造に関して、より精密で詳細な結果が得られた。

Research Products

• [Journal Article] A generalization of the Shestakov -Umirbaev inequality (2008)
  • Author(s): Shigeru Kuroda
  • Journal Title: J. Math. Soc. Japan 60 Pages: 495-510
  • NAID: 10024331742
  • Peer Reviewed
• [Journal Article] A simple proof of Nowicki's conjecture on the kernel of an elementary derivation, TMU Preprint Series (2008)
  • Author(s): Shigeru Kuroda
  • Journal Title: Tokyo J. Math. No.1(to appear) Pages: 6-6
• [Journal Article] A generalization of the Shestakov-Umirbaev inequality (2008)
  • Author(s): Shigeru Kuroda (黒田茂)
  • Journal Title: Journal 0f the Mathematical Societyof Japan 60 Pages: 495-510
  • NAID: 10024331742
  • Peer Reviewed
• [Journal Article] Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism (2008)
  • Author(s): Shigeru Kuroda (黒田茂)
  • Journal Title: Proceedings of the 3^<rd> Japan-Vietnam Joint Seminar on Commutative Algebra 掲載決定 Pages: 110-144
  • NAID: 110007608286
• [Journal Article] Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism (2008)
  • Author(s): Shigeru Kuroda(黒田茂)
  • Journal Title: Tokyo Metropolitan Univ. Math. Preprint Series No.1 Pages: 1-48
  • NAID: 110007608286
• [Journal Article] A simple proof of Nowicki's conjecture on the kernel of an elementary derivation (2008)
  • Author(s): Shigeru Kuroda(黒田茂)
  • Journal Title: Tokyo Metropolitan Univ. Math. Preprint Series No.2 Pages: 1-6
• [Journal Article] Hilbert's Fourteenth Problem and algebraic extensions with an appendix on Roberts type counterexamples (2007)
  • Author(s): Shigeru Kuroda
  • Journal Title: Acta Math. Vietnamica 32 Pages: 247-257
  • Peer Reviewed
• [Journal Article] Hilbert's fourteenth problem and algebraic extensions with an appendix on Roberts type counterexamples (2007)
  • Author(s): Shigeru Kuroda(黒田茂)
  • Journal Title: Acta Mathematica Vietnamica 32 Pages: 247-257
  • Peer Reviewed
• [Journal Article] A generalization of the Shestakov-Umirbaev inequality (2007)
  • Author(s): Shigeru Kuroda(黒田茂)
  • Journal Title: ArXiv. org(ウエブ上のプレプリント・アーカイブ) arXiv:0707-1361 Pages: 1-12
  • NAID: 10024331742
• [Journal Article] Automorphisms of a polynomial ring which admit reductions of type I (2007)
  • Author(s): Shigeru Kuroda(黒田茂)
  • Journal Title: ArXiv. org(ウエブ上のプレプリント・アーカイブ) arXiv:0708-2120 Pages: 1-11
• [Journal Article] Automorphisms of a polynomial ring which admit reductions of type I, arXiv : math. AC/0708
  • Author(s): Shigeru Kuroda
  • Journal Title: Publ. Res. Inst. Math. Sci. 2120(to appear) Pages: 11-11
• [Journal Article] Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism, arXiv : math.
  • Author(s): Shigeru Kuroda
  • Journal Title: AC/0801.0117(査読付きの専門誌に投稿中) Pages: 52-52
• [Journal Article] Initial algebras and polynomial automorphisms
  • Author(s): Shigeru Kuroda
  • Journal Title: Proceedings of the 4^<th> Japan-Vietnam Joint Seminar on Commutative Algebra (to appear)
• [Journal Article] A simple proof of Nowicki's conjecture on the kernel of an elementary derivation
  • Author(s): Shigeru Kuroda (黒田茂)
  • Journal Title: Tokyo Journal of Mathematics (掲載決定)
  • Peer Reviewed
• [Journal Article] Automorphisms of a polynomial ring which admitreductions of type 1
  • Author(s): Shigeru Kuroda (黒田茂)
  • Journal Title: Publications of the Research Institute for Mathematical Sciences (掲載決定)
  • Peer Reviewed
• [Presentation] Polynomial automorphisms and initial algebras (2009)
  • Author(s): 黒田茂
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-29
• [Presentation] Polynomial automorphisms and Initial algebras (2009)
  • Author(s): 黒田茂
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-29
• [Presentation] 正標数の体上の多項式環のtame自己同型のある特徴 (2009)
  • Author(s): 黒田茂
  • Organizer: アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学
  • Year and Date: 2009-03-16
• [Presentation] 正標数の体上の多項式環のtame自己同型のある特徴 (2009)
  • Author(s): 黒田 茂
  • Organizer: アフィン代数幾何学シンポジウム
  • Place of Presentation: 関西学院大学梅田キャンパス
  • Year and Date: 2009-03-16
• [Presentation] Initial algebras and polynomial automorphisms (2009)
  • Author(s): Shigeru Kuroda
  • Organizer: The 4^<th> Japan-Vietnam Joint Seminar on Commutative Algebra
  • Place of Presentation: 明治大学
  • Year and Date: 2009-02-21
• [Presentation] Initial algebras and polynomial automorphisms (2009)
  • Author(s): Shigeru Kuroda(黒田 茂)
  • Organizer: The Fourth Japan-Vietnam Joint Seminar on Commutative Algebra
  • Place of Presentation: 明治大学生田キャンパス
  • Year and Date: 2009-02-21
• [Presentation] 鏡映群とニュートン多面体 (2009)
  • Author(s): 黒田茂
  • Organizer: 研究会「多項式環とその周辺の諸問題」
  • Place of Presentation: 兵庫県立大学
  • Year and Date: 2009-02-14
• [Presentation] 鏡映群とニュートン多面体 (2009)
  • Author(s): 黒田茂
  • Organizer: 多項式環とその周辺の諸問題
  • Place of Presentation: 兵庫県立大学
  • Year and Date: 2009-02-14
• [Presentation] The Shestakov-Umirbaev inequality and polynomial automorphisms (2008)
  • Author(s): Shigeru Kuroda
  • Organizer: Conference on Affine Algebraic Geometry
  • Place of Presentation: Fireflies Intercultural Center, India
  • Year and Date: 2008-12-23
• [Presentation] The Shes takov-Umirbaev inequality and polynomial auto-morphisms (2008)
  • Author(s): Shigeru Kuroda(黒田 茂)
  • Organizer: Conference on Affine Algebraic Geo-metry
  • Place of Presentation: Fireflies Intercultural Center (インド)
  • Year and Date: 2008-12-23
• [Presentation] A simple proof of Nowicki's conjecture on the kernel of an elementary derivation (2008)
  • Author(s): 黒田茂
  • Organizer: 第30回可換環論シンポジウム
  • Place of Presentation: 国民宿舎虹ノ松原ホテル
  • Year and Date: 2008-11-18
• [Presentation] A simple proof of Nowicki's conjecture on the kernel of an elementary derivation (2008)
  • Author(s): 黒田茂
  • Organizer: 第30回可換環論シンポジウム
  • Place of Presentation: 国民宿舎虹ノ松原ホテル(佐賀県)
  • Year and Date: 2008-11-18
• [Presentation] Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism (2008)
  • Author(s): Shigeru Kuroda
  • Organizer: Fall Central Section Meeting of AMS
  • Place of Presentation: Western Michigan University, USA
  • Year and Date: 2008-10-18
• [Presentation] Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism (2008)
  • Author(s): Shigeru Kuroda (黒田 茂)
  • Organizer: Meeting #1043 : 2008 Fall Central Sec-tion Meeting of AMS, Affine Algebraic Geometry Session
  • Place of Presentation: Western Michigan Univ.
  • Year and Date: 2008-10-18
• [Presentation] 多項式環の自己同型とイニシャル代数 (2008)
  • Author(s): 黒田茂
  • Organizer: アフィン代数幾何学シンポジウム
  • Place of Presentation: 関西学院大学
  • Year and Date: 2008-09-15
• [Presentation] 多項式環の自己同型とイニシャル代数 (2008)
  • Author(s): 黒田茂
  • Organizer: アフィン代数幾何学シンポジウム
  • Place of Presentation: 関西学院大学梅田キャンパス
  • Year and Date: 2008-09-05
• [Presentation] 多項式環の冒険 (2008)
  • Author(s): 黒田茂
  • Organizer: 代数・表現論セミナー
  • Place of Presentation: 立命館大学
  • Year and Date: 2008-05-29
• [Presentation] 多項式環の自己同型に関する永田予想とShestakov-Umirbaev簡約 (2008)
  • Author(s): 黒田茂
  • Organizer: 日本数学会年会
  • Place of Presentation: 近畿大学
  • Year and Date: 2008-03-26
• [Presentation] 多項式環の自己同型に関する永田予想とShestakov-Umirbaev簡約 (2008)
  • Author(s): 黒田 茂
  • Organizer: 日本数学会年会(代数学分科会一般講演)
  • Place of Presentation: 近畿大学
  • Year and Date: 2008-03-26
• [Presentation] Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism (2008)
  • Author(s): Shigeru Kuroda
  • Organizer: International Conference on Commutative Algebra
  • Place of Presentation: 横浜開港記念会館
  • Year and Date: 2008-03-20
• [Presentation] 多項式環の自己同型に関する永田予想とShestakov-Umirbaev簡約(その1),(その2),(その3) (2008)
  • Author(s): 黒田茂
  • Organizer: 代数学研究会
  • Place of Presentation: 関西学院大学
  • Year and Date: 2008-03-12
• [Presentation] 多項式環の自己同型に関する永田予想とShestakov-Umirbaev簡約(その1),(その2),(その3) (2008)
  • Author(s): 黒田 茂
  • Organizer: 代数学研究会
  • Place of Presentation: 関西学院大学梅田キャンパス
  • Year and Date: 2008-03-12
• [Presentation] 基本微分の核に関するNowicki予想の簡単な別証明 (2008)
  • Author(s): 黒田 茂
  • Organizer: 代数学研究会
  • Place of Presentation: 関西学院大学梅田キャンパス
  • Year and Date: 2008-03-11
• [Presentation] 多項式環の自己同型に関する永田予想とShestakov-Umirbaev簡約 (2008)
  • Author(s): 黒田茂
  • Organizer: 複素幾何セミナー
  • Place of Presentation: 首都大学東京
  • Year and Date: 2008-01-30
• [Presentation] 多項式環の自己同型に関する永田予想とShestakov-Umirbaev簡約 (2007)
  • Author(s): 黒田茂
  • Organizer: 代数幾何学セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2007-12-14
• [Presentation] 多項式環の自己同型に関する永田予想とShestakov-Umirbaev簡約 (2007)
  • Author(s): 黒田 茂
  • Organizer: 東北大学代数幾何セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2007-12-14
• [Presentation] The Shestakov-Umirbaev inequality and automorphisms of a polynomial ring (2007)
  • Author(s): Shigeru Kuroda
  • Organizer: The 3^<rd> Japan-Vietnam Joint Seminar on Commutative Algebra
  • Place of Presentation: Institute of Mathematics, Vietnam
  • Year and Date: 2007-12-05
• [Presentation] The Shestakov-Umirbaev inequality and automorphisms of a polynomialring (2007)
  • Author(s): 黒田 茂
  • Organizer: The Third Japan-Vietnam Joint Seminar on Commutative Algebra
  • Place of Presentation: Institute of Mathematicsベトナム
  • Year and Date: 2007-12-05
• [Presentation] Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism (2007)
  • Author(s): 黒田茂
  • Organizer: 第29回可換環論シンポジウム
  • Place of Presentation: 愛知厚生年金会館ウェルシティなごや
  • Year and Date: 2007-11-22
• [Presentation] 多項式環のI型簡約可能自己同型 (2007)
  • Author(s): 黒田茂
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-23
• [Presentation] 多項式環のI型簡約可能自己同型 (2007)
  • Author(s): 黒田 茂
  • Organizer: 日本数学会秋季総合分科会(代数学分科会一般講演)
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-23
• [Presentation] Automorphisms of polynomial rings which admit reductions of type I (2007)
  • Author(s): 黒田茂
  • Organizer: 第52回代数学シンポジウム
  • Place of Presentation: 神戸大学
  • Year and Date: 2007-08-09
• [Presentation] Automorphisms of a polynomial ring which admit reductions of type I (2007)
  • Author(s): 黒田 茂
  • Organizer: 第52回代数学シンポジウム
  • Place of Presentation: 神戸大学
  • Year and Date: 2007-08-09
• [Presentation] 多項式環の自己同型と不等式 (2007)
  • Author(s): 黒田茂
  • Organizer: 代数幾何学セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2007-07-13
• [Presentation] 多項式環の自己同型と不等式 (2007)
  • Author(s): 黒田 茂
  • Organizer: 東北大学代数幾何セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2007-07-13
• [Presentation] How to construct counterexamples to Hilbert's 14th problem easily (2007)
  • Author(s): Shigeru Kuroda
  • Organizer: BIRS Workshop 07w5505 : Commutative Algebra and its Interaction with Algebraic Geometry
  • Place of Presentation: Banff Center, Canada
  • Year and Date: 2007-06-14
• [Presentation] How to construct counterexamples to Hilbert's 14th problem easily (2007)
  • Author(s): 黒田 茂
  • Organizer: BIRS Workshop 07w5505: Commutative Algebra and its Interaction with Algebraic Geometry
  • Place of Presentation: The Banff Centreカナダ
  • Year and Date: 2007-06-14
• [Presentation] Automorphisms of the polynomial ring in three variables which admit reductions of type I (2007)
  • Author(s): 黒田茂
  • Organizer: 日大特異点論セミナー
  • Place of Presentation: 日本大学
  • Year and Date: 2007-05-21
• [Presentation] Automorphisms of the polynomial ring in three variables which admitreductions of type I (2007)
  • Author(s): 黒田 茂
  • Organizer: 日大特異点論セミナー
  • Place of Presentation: 日本大学
  • Year and Date: 2007-05-21
• [Presentation] 多項式環の冒険-ヒルベルトの第14問題、SAGBI基底、自己同型 (2007)
  • Author(s): 黒田茂
  • Organizer: 数理情報科学専攻談話会・複素幾何セミナー(共催)
  • Place of Presentation: 首都大学東京
  • Year and Date: 2007-05-09
• [Presentation] 多項式環の冒険 (2007)
  • Author(s): 黒田 茂
  • Organizer: 首都大学東京数理情報科学専攻談話会
  • Place of Presentation: 首都大学東京
  • Year and Date: 2007-05-09
• [Presentation] 多項式環の自己同型に関する永田予想とShestakov-Umirbaev簡約 (2007)
  • Author(s): 黒田 茂
  • Organizer: 首都大学東京数理情報科学専複素幾何セミナー
  • Place of Presentation: 首都大学東京
  • Year and Date: 2007-01-30