Unipotent dimension and structures of algebraic varieties

2008 Fiscal Year Final Research Report

• Project/Area Number: 18540058
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Kwansei Gakuin University
• Principal Investigator: MIYANISHI Masayoshi Kwansei Gakuin University, 理工学部, 教授 (80025311)
• Co-Investigator(Renkei-kenkyūsha): MASUDA Kayo 兵庫県立大学, 物質理学研究科, 准教授 (40280416)
• Project Period (FY): 2006 – 2008
• Keywords: ユニポテント代数群 / アフィン代数多様体 / ファイブレーション / Jacobian予想 / 不分岐射 / 多項式環 / 特異点

Research Abstract

アフィン代数多様体がもつアフィン空間のファイブレーションの相対次元の最大値としてユニポテント次元の概念を導入し,アフィン代数多様体の構造を2次元および高次元の場合について解明した.その概念を応用して,ジャコピアン予想を一般化したものを一部肯定的に解決した.

Research Products

• [Journal Article] Lifting of locally nilpotent derivations under finite homomorphism (2009)
  • Author(s): 増田佳代, 宮西正宜
  • Journal Title: Tohoku Mathematical Journal (掲載決定)
  • Peer Reviewed
• [Journal Article] Jacobian problem for singular surfaces (2009)
  • Author(s): R. V. Gurjar, 宮西正宜
  • Journal Title: Journal of Mathematics 48(印刷中)
  • Peer Reviewed
• [Journal Article] Additive group scheme actions on the integral schemes defined over discrete valuation rings (2009)
  • Author(s): 宮西正宜
  • Journal Title: Journal of Algebra, a special issue for Professor PaulRoberts (印刷中)
  • Peer Reviewed
• [Journal Article] Homogeneous locally nilpotent derivations having slices and embeddings of the affine spaces (2009)
  • Author(s): 増田佳代
  • Journal Title: Journal of Algebra 321(印刷中)
  • Peer Reviewed
• [Journal Article] Smoothness of the images of the members of a linear pencil under an endomorphism of the affine plane (2009)
  • Author(s): Pierrette CassoirNogues, 宮西正宜
  • Journal Title: Journal of Pure and Applied Algebra 213 Pages: 711-723
  • Peer Reviewed
• [Journal Article] Ga-actions and completions (2008)
  • Author(s): 宮西正宜
  • Journal Title: Journal of Algebra 319 Pages: 2845-2854
  • Peer Reviewed
• [Journal Article] Affine lines on affine surfaces and the Makar-Limanov invariant (2008)
  • Author(s): R. V. Gudar, 増田佳代, 宮西正宜, P. Russell
  • Journal Title: Candian Journal of Mathematics 60 Pages: 109-139
  • Peer Reviewed
• [Journal Article] Q-factorial subalgebras of polynomial rings (2007)
  • Author(s): 宮西正宜
  • Journal Title: Acta Mathematica Vietnamica 32 Pages: 113-122
  • Peer Reviewed
• [Journal Article] Recent developments in affine algebraic geometry, Affine Algebraic Geometry edited by T. Hibi (2007)
  • Author(s): 宮西正宜
  • Journal Title: Osaka University Press Pages: 307-378
  • Peer Reviewed
• [Journal Article] A geometric approach to the Jacobian conjecture in dimension two (2006)
  • Author(s): 宮西正宜
  • Journal Title: Journal of Algebra 304 Pages: 1014-1025
  • Peer Reviewed
• [Journal Article] Affine pseudo-planes with torus actions (2006)
  • Author(s): 増田佳代, 宮西正宜
  • Journal Title: Transformation Groups 11 Pages: 249-267
  • Peer Reviewed
• [Presentation] Additive group scheme actions on integral domains defined discrete valuation rings (2008)
  • Author(s): 宮西正宜
  • Organizer: Conference on Affine Algebraic Geometry
  • Place of Presentation: Bangalore, India
  • Year and Date: 2008-12-23
• [Presentation] Jacobian Problem for singular surfaces (2008)
  • Author(s): 宮西正宜
  • Organizer: Affine geometry, Number theory and Singularities, Pi60
  • Place of Presentation: CIEM, Castro Urdiales, Spain
  • Year and Date: 2008-06-17
• [Presentation] Ga-actions andcompletions (2007)
  • Author(s): 宮西正宜
  • Organizer: Affine Algebraic Geometry, Special session of the Western section of American Mathematical Society
  • Place of Presentation: New Mexico University, Albuquerque, USA
  • Year and Date: 2007-10-13
• [Presentation] Geometry of open algebraic surfaces (2007)
  • Author(s): 宮西正宜
  • Organizer: Workshop on Affine Algebraic Geometry
  • Place of Presentation: athematisches Forschungsinstitut Oberwolfach, Germany
  • Year and Date: 2007-01-09
• [Presentation] pure subalgebras of a polynomial ring and related topics (2006)
  • Author(s): 宮西正宜
  • Organizer: International School and Workshop on Polynomial Automorphisms and Related Topics
  • Place of Presentation: Hanoi, Vietnam
  • Year and Date: 2006-10-19
• [Presentation] Affine pseudo-planes with torus actions (2006)
  • Author(s): 宮西正宜
  • Organizer: Algebraic Geometry Conference ABB70
  • Place of Presentation: Bedlewo, Poland. Banach Conference Center
  • Year and Date: 2006-07-13
• [Presentation] Quelques pensees sur le theoreme d'Ax (2006)
  • Author(s): 宮西正宜
  • Organizer: Seminaire de la Theorie des Nombres
  • Place of Presentation: Universite de Bordeaux I, France
  • Year and Date: 2006-03-24
• [Book] 現代数理入門 (2009)
  • Author(s): 宮西正宜,茨木俊秀, 編
  • Total Pages: (印刷中)
  • Publisher: 関西学院大学出版会
• [Remarks] 国内のアフィン代数幾何学研究集会を関西学院大学大阪梅田キャンパスの施設を利用して,次の3回主催した.(1)2009年3月16,17,18日(2)2008年9月3,4,5,6日(3)2008年3月10,11,12日