Commutative algebraic approach to the study of affine algebraic geometry focused on fibrations

• Project/Area Number: 21540034
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: University of Fukui
• Principal Investigator: ONODA Nobuharu 福井大学, 大学院・工学研究科, 教授 (40169347)
• Research Collaborator: BHATWADEKAR S. M. Bhaskaracharya Pratishthana, 教授 ; DUTTA A. K. Indian Statistical Institute, 教授
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 可換環論 / アフィン代数幾何学 / 国際研究者交流 / インド / アフィン代数幾何科学

Research Abstract

Some results are obtained regarding affine fibration which is an important subject both in commutative algebra and affine algebraic geometry. In particular, for an algebra obtained by patching polynomial algebras, the structure theorem is proved and isomorphism classes are determined in the case where the base ring is a factorial domain of dimension two. Furthermore, finite generation is investigated for Noetherian subalgebras of polynomial algebras.

Research Products

• [Journal Article] Commutative group algebras whose quotient rings by nilradical are generated by idempotents (2011)
  • Author(s): H. Kawai and N. Onoda
  • Journal Title: Rocky Mountain J. Math. Volume: Vol.41 Pages: 229-238
  • NAID: 120006555341
  • Peer Reviewed
• [Journal Article] Commutative group algebras whose quotient rings by nilradicals are generated by idempotents (2011)
  • Author(s): H.Kawai, N.Onoda
  • Journal Title: Rocky Mountain Journal of Mathematics Volume: 41 Pages: 229-238
  • NAID: 120006555341
  • Peer Reviewed
• [Journal Article] On algebras which are locally A^1 in codimension-one
  • Author(s): S. M. Bhatwadekar, A. K. Dutta and N. Onoda
  • Journal Title: Trans. Amer. Math.
  • Peer Reviewed
• [Presentation] Some results on polynomial fibrations over two-dimensional normal domains (2011)
  • Author(s): N. Onoda
  • Organizer: 第8回アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学大阪梅田キャンパス
  • Year and Date: 2011-09-02
• [Presentation] Some results on polynomial fibrations over two-dimensional normal domains (2011)
  • Author(s): N.Onoda
  • Organizer: 第8回アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学大阪梅田キャンパス(招待講演)
  • Year and Date: 2011-09-02
• [Presentation] Some results on finite generation of algebras of certain type (2011)
  • Author(s): N.Onoda
  • Organizer: Math.Colloquium at TIFR
  • Place of Presentation: Tata Institute of Fundamental Research(招待講演)
  • Year and Date: 2011-03-17
• [Presentation] Some patching results on algebras over two-dimensional factorial domains (2010)
  • Author(s): N. Onoda
  • Organizer: 第6回アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学大阪梅田キャンパス
  • Year and Date: 2010-09-05
• [Presentation] Some patching results on algebras over two-dimensional factorial domains (2010)
  • Author(s): 小野田信春
  • Organizer: アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学大阪梅田キャンパス
  • Year and Date: 2010-09-05
• [Presentation] Some remarks on A^1-fibrations in codimension-one (2009)
  • Author(s): N. Onoda
  • Organizer: 第4回アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学大阪梅田キャンパス
  • Year and Date: 2009-09-03
• [Presentation] Some remarks on A1-fibrations in codimension-one (2009)
  • Author(s): Nobuharu Onoda
  • Organizer: アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学大阪梅田キャンパス
  • Year and Date: 2009-09-03
• [Book] 基礎から学ぶ線形代数 (2010)
  • Author(s): 黒木哲徳、小野田信春、古閑義之、芹生正史、高木丈夫、保倉理美
  • Total Pages: 185
  • Publisher: 共立出版
• [Remarks]
  • URL: http://apphy.u-fukui.ac.jp/mqs/math/onoda.html