Performance information

• A new proof of the non-tameness of the Nagata automorphism from the point of view of the Sarkisov program　　　　　　　　　　　　　　　
  Takashi Kishimoto
  COMPOSITIO MATHEMATICA, Volume：144, Number：4, First page：963, Last page：977, Jul. 2008
  The Nagata automorphism is a kind of complicated automorphism on the affine 3-space C(3). For a long time, it remained unknown whether or not the Nagata automorphism is tame until Shestakov and Umirbaev at last proved that it is not tame in 2004. by purely algebraic methods (e.g. Poisson algebra). In this paper, we consider a certain necessary condition for a given automorphism on C(3) to be tame from the point of view of the Sarkisov program established by Corti. Furthermore, by using it, we shall give a new algebro-geometric proof of the non-tameness of the Nagata automorphism.
  LONDON MATH SOC, English
  DOI：https://doi.org/10.1112/S0010437X07003399
  DOI ID：10.1112/S0010437X07003399, ISSN：0010-437X, Web of Science ID：WOS:000259119200008
• A new proof of the non-tameness of the Nagata automorphism from the point of view of the Sarkisov program　　　　　　　　　　　　　　　
  Takashi Kishimoto
  Compositio Mathematica, Volume：144, Number：4, First page：963, Last page：977, Jul. 2008
  The Nagata automorphism is a kind of complicated automorphism on the affine 3-space C 3. For a long time, it remained unknown whether or not the Nagata automorphism is tame until Shestakov and Umirbaev at last proved that it is not tame in 2004, by purely algebraic methods (e.g.Poisson algebra). In this paper, we consider a certain necessary condition for a given automorphism on C3 to be tame from the point of view of the Sarkisov program established by Corti. Furthermore, by using it, we shall give a new algebro-geometric proof of the non-tameness of the Nagata automorphism. © 2008 Copyright Foundation Compositio Mathematica 2008.
  English
  DOI：https://doi.org/10.1112/S0010437X07003399
  DOI ID：10.1112/S0010437X07003399, ISSN：0010-437X, SCOPUS ID：47749137363
• Affine lines on Q-homology planes with logarithmic kodaira dimension -infinity (vol 13, pg 1, 2008)　　　　　　　　　　　　　　　
  Takashi Kishimoto; Hideo Kojima
  TRANSFORMATION GROUPS, Volume：13, Number：1, First page：211, Last page：213, Mar. 2008
  BIRKHAUSER BOSTON INC, English, Others
  DOI：https://doi.org/10.1007/s00031-008-9007-z
  DOI ID：10.1007/s00031-008-9007-z, ISSN：1083-4362, Web of Science ID：WOS:000257394300009
• Affine lines on Q-homology planes with logarithmic kodaira dimension -infinity　　　　　　　　　　　　　　　
  Takashi Kishimoto; Hideo Kojima
  Volume：13, Number：1, First page：211, Last page：213, 2008
  DOI：https://doi.org/10.1007/s00031-008-9007-z
  DOI ID：10.1007/s00031-008-9007-z
• ログ極小モデル理論の観点からの３次元アフィン代数多様体の双正則的構造解析　　　　　　　　　　　　　　　
  岸本崇
  Volume：5 (平成18年度), First page：486, Last page：487, 2007
• Affine threefolds whose log canonical bundles are not numerically effective　　　　　　　　　　　　　　　
  Takashi Kishimoto
  JOURNAL OF PURE AND APPLIED ALGEBRA, Volume：208, Number：1, First page：189, Last page：204, Jan. 2007
  Let X hooked right arrow (T, D) be a compactification of an affine 3-fold X into a smooth projective 3-fold T such that the (reduced) boundary divisor D is SNC. In this paper, as an affine counterpart to the work due to S. Mori (cf. [S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982) 133-176]), we shall classify (K + D)-negative extremal rays on T. In particular, if such an extremal ray R = R+[C] intersects K non-negatively, we shall describe the log flips and divisorial contractions appearing explicitly. (c) 2005 Elsevier B.V. All rights reserved.
  ELSEVIER SCIENCE BV, English
  DOI：https://doi.org/10.1016/j.jpaa.2005.12.007
  DOI ID：10.1016/j.jpaa.2005.12.007, ISSN：0022-4049, Web of Science ID：WOS:000242650900017
• ログ極小モデル理論の観点からの３次元アフィン代数多様体の双正則的構造解析　　　　　　　　　　　　　　　
  岸本崇
  総合研究機構研究プロジェクト研究成果報告書, Volume：5 (平成18年度), First page：486, Last page：487, 2007
• Affine threefolds whose log canonical bundles are not numerically effective　　　　　　　　　　　　　　　
  Takashi Kishimoto
  Journal of Pure and Applied Algebra, Volume：208, Number：1, First page：189, Last page：204, Jan. 2007
  Let X {right arrow, hooked} (T, D) be a compactification of an affine 3-fold X into a smooth projective 3-fold T such that the (reduced) boundary divisor D is SNC. In this paper, as an affine counterpart to the work due to S. Mori (cf. [S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982) 133-176]), we shall classify (K + D)-negative extremal rays on T. In particular, if such an extremal ray R = R+ [C] intersects K non-negatively, we shall describe the log flips and divisorial contractions appearing explicitly. © 2005 Elsevier Ltd. All rights reserved.
  English
  DOI：https://doi.org/10.1016/j.jpaa.2005.12.007
  DOI ID：10.1016/j.jpaa.2005.12.007, ISSN：0022-4049, SCOPUS ID：33750433579
• The combination of 3-dimensional Affine Algebraic Geometry and Minimal Model Program　　　　　　　　　　　　　　　
  岸本崇
  Volume：4 (平成17年度), 2006
• On the logarithmic kodaira dimension of affine threefolds　　　　　　　　　　　　　　　
  Takashi Kishimoto
  International Journal of Mathematics, Volume：17, Number：1, First page：1, Last page：17, Jan. 2006
  In this article, we shall consider how to analyze affine threefolds associated to the log Kodaira dimension K and make the framework for this purpose under a certain geometric condition. As a consequence of our main result, under this geometric condition, we can describe the construction of affine threefolds with κ̄ = ∞- fairly explicitly, and show that affine threefolds with κ̄ = 2 have the structure of ℂ*-fibrations. © World Scientific Publishing Company.
  English
  DOI：https://doi.org/10.1142/S0129167X06003382
  DOI ID：10.1142/S0129167X06003382, ISSN：0129-167X, SCOPUS ID：32644438679
• The combination of 3-dimensional Affine Algebraic Geometry and Minimal Model Program　　　　　　　　　　　　　　　
  岸本崇
  総合研究機構研究プロジェクト研究成果報告書, Volume：4 (平成17年度), 2006
• Affine lines on Q-homology planes with logarithmic Kodaira dimension-infinity　　　　　　　　　　　　　　　
  Takashi Kishimoto; Hideo Kojima
  TRANSFORMATION GROUPS, Volume：11, Number：4, First page：659, Last page：672, 2006
  In the present paper, we study a topologically contractible irreducible algebraic curve C on a Q-homology plane S with kappa(S) = -infinity. We determine such a pair (S, C) when kappa(S\C) >= 0 and C is smooth. Moreover, we prove that if C is not smooth, then C has exactly one singular point and the Makar-Limanov invariant of S is trivial.
  BIRKHAUSER BOSTON INC, English
  DOI：https://doi.org/10.1007/s00031-005-1121-6
  DOI ID：10.1007/s00031-005-1121-6, ISSN：1083-4362, Web of Science ID：WOS:000242724000005
• On the logarithmic Kodaira dimension of affine threefolds　　　　　　　　　　　　　　　
  Kishimoto, Takashi
  International Journal of Mathematics, Volume：17, Number：1, First page：1, Last page：17, 2006
  DOI：https://doi.org/10.1142/S0129167X06003382
  DOI ID：10.1142/S0129167X06003382
• Compactifications of contractible affine 3-folds into smooth Fano 3-folds with B 2=2　　　　　　　　　　　　　　　
  Takashi Kishimoto
  Mathematische Zeitschrift, Volume：251, Number：4, First page：783, Last page：820, Dec. 2005
  After the contributions of Furushima, Nakayama, Peternell and Schneider, in 1993, Furushima [Fur93] finally succeeded in the classification of the compactifications of the affine 3-space [InlineMediaObject not available: see fulltext.] into smooth Fano 3-folds with B 2=1. In this paper, we consider the compactifications of the contractible affine 3-folds X (not necessarily X=[InlineMediaObject not available: see fulltext.]) into smooth Fano 3-folds V with B 2=2. Consequently, we classify all such compactifications X →(V,D 1⊃D 2) in the case where K V +D 1+D 2 is not nef. Furthermore, we see that infinitely many mutually non-isomorphic exotic [InlineMediaObject not available: see fulltext.]'s can be compactified into Fano 3-folds with B 2=2. This phenomenon never occurs when B 2=1. © Springer-Verlag 2005.
  English
  DOI：https://doi.org/10.1007/s00209-005-0831-8
  DOI ID：10.1007/s00209-005-0831-8, ISSN：0025-5874, SCOPUS ID：27844499265
• Compactifications of contractible affine 3-folds into smooth Fano 3-folds with B-2=2　　　　　　　　　　　　　　　
  T Kishimoto
  MATHEMATISCHE ZEITSCHRIFT, Volume：251, Number：4, First page：783, Last page：820, Dec. 2005
  After the contributions of Furushima, Nakayama, Peternell and Schneider, in 1993, Furushima [Fur93] finally succeeded in the classification of the compactifications of the affine 3-space A(3) into smooth Fano 3-folds with B-2 = 1. In this paper, we consider the compactifications of the contractible affine 3-folds X (not necessarily X = A(3)) into smooth Fano 3-folds V with B-2 = 2. Consequently, we classify all such compactifications X --> (V, D-1 boolean OR D-2) in the case where K-V + D-1+ D-2 is not nef. Furthermore, we see that infinitely many mutually non-isomorphic exotic A(3)' s can be compactified into Fano 3-folds with B-2 = 2. This phenomenon never occurs when B-2 = 1.
  SPRINGER, English
  DOI：https://doi.org/10.1007/s00209-005-0831-8
  DOI ID：10.1007/s00209-005-0831-8, ISSN：0025-5874, Web of Science ID：WOS:000233043900004
• Analysis of the structure of affine algebraic threefolds from a point of view of MinimalModel Theory (Mori Theory)　　　　　　　　　　　　　　　
  岸本崇
  Volume：3 (平成16年度), 2005
• The explicit factorization of the Cremona transformation which is an extension of the Nagata automorphism into elementary links　　　　　　　　　　　　　　　
  Takashi Kishimoto
  Mathematische Nachrichten, Volume：278, Number：7-8, First page：833, Last page：843, 2005
  We consider the Cremona transformation Φσ: ℙ3⋯ → ℙ3which is an extension of the famous Nagata automorphism σ on the affine 3-space double-struck A sign3. In this paper we shall factorize this Cremona transformation Φσ explicitly into 8 elementary links according to the Sarkisov Program. © 2005 WILEY-VCH Verlag GmbH &
  Co. KGaA, Weinheim.
  English
  DOI：https://doi.org/10.1002/mana.200310276
  DOI ID：10.1002/mana.200310276, ISSN：0025-584X, SCOPUS ID：20444426541
• Singularities on normal affine 3-folds containing A(1)-cylinderlike open subsets　　　　　　　　　　　　　　　
  T Kishimoto
  AFFINE ALGEBRAIC GEOMETRY, Volume：369, First page：139, Last page：163, 2005
  The normal affine varieties with A(1)-cylinderlike open subsets play important roles and of interest in itself in affine algebraic geometry. In [Miy81], Miyanishi described the construction of normal affine surfaces Y with A(1)-cylinderlike open subsets, explicitly. According to this explicit construction, he also has shown that such surfaces Y have at most cyclic quotient singularities. In this article, we consider the 3-dimensional generalization of the Miyanishi's result. Namely, we shall investigate how to construct normal affine 3-folds X containing A(1)-cylinderlike open subsets and the possibility of singularities on such X under a certain geometric assumption concerning the compactifications.
  AMER MATHEMATICAL SOC, English
  ISSN：0271-4132, Web of Science ID：WOS:000227464800009
• Analysis of the structure of affine algebraic threefolds from a point of view of MinimalModel Theory (Mori Theory)　　　　　　　　　　　　　　　
  岸本崇
  総合研究機構研究プロジェクト研究成果報告書, Volume：3 (平成16年度), 2005
• The explicit factorization of the Cremona transformation which is an extension of the Nagata automorphism into elementary links　　　　　　　　　　　　　　　
  T Kishimoto
  MATHEMATISCHE NACHRICHTEN, Volume：278, Number：7-8, First page：833, Last page：843, 2005
  We consider the Cremona transformation Phi(sigma) : P-3... -> P-3 which is an extension of the famous Nagata automorphism sigma on the affine 3-space A(3). In this paper we shall factorize this Cremona transformation Phi(sigma) explicitly into 8 elementary links according to the Sarkisov Program. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
  WILEY-V C H VERLAG GMBH, English
  DOI：https://doi.org/10.1002/mana.200310276
  DOI ID：10.1002/mana.200310276, ISSN：0025-584X, Web of Science ID：WOS:000229699100008
• Singularities on normal affine 3-folds containing A1-cylinderlike open subsets　　　　　　　　　　　　　　　
  Kishimoto, Takashi
  Contemporary Mathematics, Volume：369, First page：139, Last page：163, 2005
• On the compactifications of contractible affine threefolds and the Zariski Cancellation Problem　　　　　　　　　　　　　　　
  Takashi Kishimoto
  Mathematische Zeitschrift, Volume：247, Number：1, First page：149, Last page：181, May 2004
  In this article, we consider the compactifications of some kinds of contractible smooth affine threefolds and the characterization of the affine 3-space double-struck A sign3 keeping the 3-dimensional Zariski Cancellation Problem in mind. We classify the compactifications of contractible smooth affine threefolds with a certain condition concerning the numerical property of boundary divisors with respect to compactifications and, then, we show that if an affine threefold X satisfies X × double-struck A sign 1 ≅ double-struck A sign4 and this numerical condition, then X is isomorphic to the affine 3-space double-struck A sign 3.
  English
  DOI：https://doi.org/10.1007/s00209-003-0635-7
  DOI ID：10.1007/s00209-003-0635-7, ISSN：0025-5874, SCOPUS ID：2442590830
• On the compactifications of contractible affine threefolds and the Zariski Cancellation Problem　　　　　　　　　　　　　　　
  T Kishimoto
  MATHEMATISCHE ZEITSCHRIFT, Volume：247, Number：1, First page：149, Last page：181, May 2004
  In this article, we consider the compactifications of some kinds of contractible smooth affine threefolds and the characterization of the affine 3-space A(3) keeping the 3-dimensional Zariski Cancellation Problem in mind. We classify the compactifications of contractible smooth affine threefolds with a certain condition concerning the numerical property of boundary divisors with respect to compactifications and, then, we show that if an affine threefold X satisfies X x A(1) congruent to A(4) and this numerical condition, then X is isomorphic to the affine 3-space A(3).
  SPRINGER-VERLAG, English
  DOI：https://doi.org/10.1007/s00209-003-0635-7
  DOI ID：10.1007/s00209-003-0635-7, ISSN：0025-5874, Web of Science ID：WOS:000220713800007
• Abhyankar-Sathaye Embedding Problem in dimension three　　　　　　　　　　　　　　　
  Kishimoto, Takashi
  Volume：42, First page：641, Last page：669, 2002
• A new proof of a theorem of Ramanujam-Morrow　　　　　　　　　　　　　　　
  Kishimoto, Takashi
  Volume：42, First page：117, Last page：139, 2002
• Abhyankar-Sathaye Embedding Problem in dimension three　　　　　　　　　　　　　　　
  Kishimoto, Takashi
  Journal of Mathematics of Kyoto University, Volume：42, First page：641, Last page：669, 2002
• A new proof of a theorem of Ramanujam-Morrow　　　　　　　　　　　　　　　
  Takashi Kishimoto
  Kyoto Journal of Mathematics, Volume：42, Number：1, First page：117, Last page：139, 2002
  Morrow classified all weighted dual graphs of the boundary of the minimal normal compactifications of the affine plane A2 by using a result of Ramanujam that any minimal normal compactification of A2 has a linear chain as the graph of the boundary divisor. In this article, we give a new proof of the above-mentioned results of Ramanujam-Morrow from a different point of view and by the purely algebro-geometric arguments. Moreover, we show that the affine plane A2 is characterized by the weighted dual graph of the boundary divisor.
  Kyoto University, English
  DOI：https://doi.org/10.1215/kjm/1250284714
  DOI ID：10.1215/kjm/1250284714, ISSN：0023-608X, SCOPUS ID：0036520891
• Projective plane curves whose complements have logarithmic Kodaira dimension one　　　　　　　　　　　　　　　
  Takashi Kishimoto
  Japanese Journal of Mathematics, Volume：27, Number：2, First page：275, Last page：310, 2001
  English
  DOI：https://doi.org/10.4099/math1924.27.275
  DOI ID：10.4099/math1924.27.275, ISSN：0289-2316, SCOPUS ID：33847645456
• Projective plane curves whose complements have logarithmic Kodaira dimension one　　　　　　　　　　　　　　　
  Kishimoto, Takashi
  Japanese Journal of Mathematics, Volume：27, First page：275, Last page：310, 2001

• ログ極小モデルプログラムの視点からの３次元アフィン代数多様体の構造解析　　　　　　　　　　　　　　　
  Competitive research funding
• -　　　　　　　　　　　　　　　
  Competitive research funding