Organization
Undergraduate School School of Science and Technology Professor
Title
Professor
External link
Degree
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博士(理学) ( 1994.9 東京都立大学 )
Research Areas
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Natural sciences / Algebra / 代数学(Algebra)
Education
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Tokyo Metropolitan University Graduate School of Science
- 1994
Country/Region： Japan
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Tokyo Metropolitan University Graduate School, Division of Natural Science
- 1994
Country/Region： Japan
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Tokyo Metropolitan University Graduate School, Division of Natural Science
- 1994
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Saitama University Faculty of Science
- 1987
Country/Region： Japan
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Saitama University Faculty of Science
- 1987
Professional Memberships
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日本数学会
Committee Memberships
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Ｔｏｋｙｏ Ｊ Ｍａｔｈ 編集委員
2011.4 - 2013.3
Papers
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A note on the k-Buchsbaum property of symbolic powers of Stanley-Reisner ideals
N. C. Minh
Tokyo J. Math 34 2011.6
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Buchsbaumness of ordinary powers of two-dimensional square-free monomial ideals
N. C. Minh
Journal of Algebra 327 2011.5
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The Buchsbaum property of symbolic powers of Stanley-Reisner ideals of dimension 1
N. C. Minh
Journal of Pure and Applied Algebra 215 ( 2 ) 2011.1
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Unmixed monomial ideals of dimension two and their Cohen-Macaulay properties
N. C. Minh
Communications in Algebra 38 ( 5 ) 1699,1714 2010.5
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Adjoint ideals and Gorenstein blowups in two-dimensional regular local rings
E. Hyry, L.Ojala
Mathematische Zeitschrift 254 ( 4 ) 2006.6
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Rees algebras of the second syzygy module of the residue field of a regular local ring
S. Goto, K. Kurano, F. Hayasaka and Y. Nakamura
Contemporary Math. 390 2005
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The bound of the difference between parameter ideals and their tight closures
後藤四郎・中村幸男
Tokyo Journal of Mathematics 25 41-48 2002.6
MISC
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Buchsbaum property of symbolic powers of Stanley-Reisner ideals
N. C. Minh
Proceedings of the 4th Japan-Vietnam joint seminar on Commutative Algebra 2009.8
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Monomial ideals which are the core of ideals in two dimensional polynomial ring
Proceedings of the 3rd Japan-Vietnam joint seminar on Commutative Algebra 2008.6
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Multiplicity and Tight Closure of Parameters
後藤四郎(教授)
Academic PressJournal of Algebra 244 2001.9
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パラメーターイデアルの重複度とtight closure
明治大学『明治大学理工学部研究報告』 24 2001.3
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On the Buchsbaum Propenty of Associated graded rings
Y Nakamura
Academic Press Journal of Algebra 209巻 ( 1 ) 345 - 366 1998
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On the Cohen-Macaulayness of multi-Rees algebras and Rees algebras of power of ideals(共著)
B Korb, Y Nakamura
Journal of the mathematical society of Japan 50 ( 2 ) 451 - 467 1998
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On the Buchsbaum propenty of associated graded rings for certain m-primary ideals
A conference in honor of D. Buchsbaum 1998
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On the Govensteinness in graded rings associated to centain ideals of analytic deviation one(共著)
Shiro Goto, Yukio Nakamura, Koji Nishida, Koji Nishida
Japanese Journal of Mathematics 23 ( 2 ) 303 - 318 1997
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Cohen-Macaulay graded rings associated to ideals(共著)
S Goto, Y Nakamura, K Nishida
American Journal of Mathematics 118 ( 6 ) 1197 - 1213 1996
Presentations
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An extension of Grassmann algebras
2002.9
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The supremum of the difference between the multiplicity and the tight closure
◎後藤四郎(教授)
2001.11
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Parameter ideals and tight closures
◎後藤四郎(教授)
2001.8
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The multiphicity and the tight closure of a patameter ideal
◎後藤四郎(教授)
2001.3
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The multiplicity and the tight closure of a parameter ideal
2000.12
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On the Buchsbaum propenty of associated graded rings for certain m-primay ideals
1998.5
Research Projects
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Monomial ideals in polynomial rings
Grant number：23540060 2011.4 - 2016.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Nakamura Yukio, Nguen Cong Minh, HIGASHIDAIRA Hirotaka, KAWAMURA Masaya
Grant amount：\4810000 （ Direct Cost: \3700000 、 Indirect Cost：\1110000 ）
The purpose of the research is to investigate the relation between the property of simplicial complexes in Discrete Mathematics and that of Stanley-Reisner rings in Commutative Algebra.
As a result, we characterize the k-Buchsbaum property of the residue class rings of the polynomial ring by the power of Stanley-Reisner ideals. -
Rees環のF-正則性とF-有理性に関する研究
Grant number：14740028 2002.4 - 2003.3
日本学術振興会 若手研究 (B) 若手研究(B)
中村 幸男
Grant amount：\2800000 （ Direct Cost: \2800000 ）
m-準素整閉単純イデアルとそれに付随するRees環の定める射影スキームのGorenstein性について研究した。2次元正則局所環(A,m)上のm-準素整閉イデアルの単純イデアルによる一意分解性に関する研究は、Zariskiに始まり,Lipman, Hunekeらによってより深く研究されてきた。彼らの展開する理論では、イデアルの位数・付置・2次変換・ブローアップなどを使う手法が主に用いられており、特にイデアルのトランスフォームを取るという手法が本質的である。
私の目標とすることはm-準素整閉イデアルの解析である。上述の一意分解定理によりm-準素整閉単純イデアルについて解析できればいいのだが、m-準素整閉単純イデアルを調べるといってもなかなか特徴付けできるものではない。そこでトランスフォームをとると位数が1になるm-準素整閉単純イデアルを調べ、そのようなイデアルの形を決定した。その応用として、m-準素整閉単純イデアルIの定めるRees環R(I)が斉次座標環となる射影スキームProj(R(I)がGorensteinスキームとなる必要十分条件はIの位数が1となることと同値である事がわかった。 -
Study on algebraic properties of Rees algebras
Grant type：Competitive
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Study on algebraic properties of Rees algebras
Grant type：Competitive
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