Study on affine algebraic varieties and extension of the base field

• Project/Area Number: 20540040
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: University of Toyama
• Principal Investigator: ASANUMA Teruo University of Toyama, 大学院・理工学研究部(理学), 教授 (50115127)
• Co-Investigator(Renkei-kenkyūsha): ONODA Nobuharu 福井大学, 工学部, 教授 (40169347)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 開代数幾何学 / ヤコビアン予想 / 可換環 / 多項式環

Research Abstract

The Jacobian conjecture asserts that a polynomial map of the ndimensional affine space over the complex number field defined by n polynomials in n variables with the Jacobian nonzero constant must be an isomorphism. The conjecture is still open for any n>1. We study the conjecture from the algebraic and topological point of view and give several conditions equivalent to the conjecture.

Research Products

• [Journal Article] ヤコビアン予想の位相的側面 (2010)
  • Author(s): 浅沼照雄
  • Journal Title: 第54回代数学シンポジウム報告集 Pages: 99-108
• [Presentation] Topology of singularities of polynomial curves with the Jacobian non-zero constant (2010)
  • Author(s): 浅沼照雄
  • Organizer: アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学(大阪)招待
  • Year and Date: 2010-09-05
• [Presentation] Topology of singularities of polynomial curves with the Jacobian non-zero constant. (2010)
  • Author(s): 浅沼照雄
  • 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: 2010-09-05
• [Presentation] Branched covering induced by a polynomial map (2010)
  • Author(s): 浅沼照雄
  • Organizer: アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学(大阪)招待
  • Year and Date: 2010-03-06
• [Presentation] Branched covering induced by a polynomial map (2010)
  • Author(s): 浅沼照雄
  • Organizer: アファイン代数幾何学研究集会
  • Place of Presentation: 関西学院大学
  • Year and Date: 2010-03-06
• [Presentation] Topology of the image of a polynomial map (2009)
  • Author(s): 浅沼照雄
  • Organizer: アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学(大阪)招待
  • Year and Date: 2009-09-06
• [Presentation] Topology of the image of a polynomial map (2009)
  • Author(s): 浅沼照雄
  • Organizer: アファイン代数幾何学研究集会
  • Place of Presentation: 関西学院大学
  • Year and Date: 2009-09-06
• [Presentation] ヤコビアン予想の位相的側面 (2009)
  • Author(s): 浅沼照雄
  • Organizer: 日本数学会第54回代数学シンポジウム
  • Place of Presentation: 明治大学(東京)招待
  • Year and Date: 2009-08-04
• [Presentation] ヤコビアン予想の位相的側面 (2009)
  • Author(s): 浅沼照雄
  • Organizer: 日本数学会代数学分科会第54回代数学シンポジウム
  • Place of Presentation: 明治大学
  • Year and Date: 2009-08-04
• [Presentation] 国際会議Automorphisms of Affine Space Topological approach to the Jacobian Conjecture (2009)
  • Author(s): 浅沼照雄
  • Place of Presentation: ラドボード大学(オランダ)招待
  • Year and Date: 2009-07-06
• [Presentation] Topological approach to the Jacobian conjecture (2009)
  • Author(s): 浅沼照雄
  • Organizer: 国際会議Automorphisms of Affine Space
  • Place of Presentation: オランダ(ラドボード大学)
  • Year and Date: 2009-07-06
• [Presentation] Topological approach to the Jacobian Conjecture (2009)
  • Author(s): 浅沼照雄
  • Organizer: アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学(大阪)招待
  • Year and Date: 2009-03-18
• [Presentation] Topological approach to the Jacobian Conjecture (2009)
  • Author(s): 浅沼照雄
  • Organizer: アファイン代数幾何学研究集会
  • Place of Presentation: 関西学院大学(大阪)
  • Year and Date: 2009-03-18
• [Presentation] Jacobian Conjecture (2009)
  • Author(s): 浅沼照雄
  • Organizer: Mini-work shop on Algebra
  • Place of Presentation: 国立台湾大学(台湾)招待
• [Presentation] Jacobian Conjecture (2009)
  • Author(s): 浅沼照雄
  • Organizer: Mini-work shop on Algebra
  • Place of Presentation: 国立台湾大学(台湾)
• [Presentation] Topological aspect of the Jacobian Conjecture (2008)
  • Author(s): 浅沼照雄
  • Organizer: Conference on Affine algebraic geometry
  • Place of Presentation: バンガロール(インド)招待
  • Year and Date: 2008-12-28
• [Presentation] Topological aspect of the Jacobian Conjecture (2008)
  • Author(s): 浅沼照雄
  • Organizer: Conference on Affine algebraic geometry
  • Place of Presentation: Bangalore (インド)
  • Year and Date: 2008-12-28
• [Presentation] Topological aspect of the Jacobian Conjecture (2008)
  • Author(s): 浅沼照雄
  • Place of Presentation: Western Michigan University(米国)招待
  • Year and Date: 2008-10-17
• [Presentation] Topological aspect of the Jacobian Conjecture (2008)
  • Author(s): 浅沼照雄
  • Organizer: AMS Fall Central Section Meeting
  • Place of Presentation: Western Michigan University (米国)
  • Year and Date: 2008-10-17