2001 Fiscal Year Annual Research Report

退化からみた代数幾何学・Hodge理論・Log幾何学相互の関係の研究

Research Project

Project/Area Number	11304001
Research Institution	Osaka University
Principal Investigator	臼井三平大阪大学, 大学院・理学研究科, 教授 (90117002)
Co-Investigator(Kenkyū-buntansha)	向井茂京都大学, 数理解析研究所, 教授 (80115641) 加藤和也京都大学, 大学院・理学研究科, 教授 (90111450) 中村郁北海道大学, 大学院・理学研究科, 教授 (50022687) 今野一宏大阪大学, 大学院・理学研究科, 助教授 (10186869) 森重文京都大学, 数理解析研究所, 教授 (00093328)
Keywords	対数的Hodge構造 / モジュライのコンパクト化 / Torelli問題 / 代数多様体 / 標準束公式 / 標準環 / 2次包 / 特異シンプレクティック多様体
Research Abstract	以下の研究集会を開催した: 1)ミニワークショップ「代数幾何学」2001年6月2日〜4日,兵庫県八千代町公民館,世話係:臼井三平.密度の高い討議をした.また勤務時間外に地元の人達との交流をした. 2)国際シンポジュウム「Algebraic Geometry in East Asia」2001年8月3日〜10日,京都府国際高等研究所.組織委員:大渕朗、今野一宏、森脇淳、中山昇、臼井三平. 東アジアを主とする海外からの参加者15名を含む60名程の参加者が密度の濃い交流をした. 東アジア各国持ち回りの会に発展しそうである. 3)研究集会「代数幾何学シンポジウム」2001年10月22日〜26日,兵庫県立城崎大会議館,世話係:徳永浩雄,小林正典.恒例の代数幾何学全分野の集会を成功裏に開催できた. 4)研究集会「Hodge理論と代数幾何学」2001年11月27日〜29日,大阪大学,世話係:朝倉政典,臼井三平,佐竹郁夫,斎藤秀司.20年近く続いている恒例の研究集会を開催した.それぞれの研究集会の報告集を作成中である. 個々の研究実績として主なものは次の通りである:臼井と加藤は共同研究により,対数的Hodge構造のfine moduliを構成した.斎藤秀司はそれの幾何への応用を始めた.森は小平の標準束公式の一般化を与え,それにより小平次元3以下の代数多様体の標準環が有限生成出あることを示した.今野は一般型代数曲面の2次包の次元や標準環の関係式の上限を調べた.並河はある種の特異シンプレクティック多様体の周期写像を大域的に調べ,Torelli問題に対する反例を構成した. 本科研費の代表者・分担者によるその他の成果については発表論文表参照.

Research Products
(25 results)

All Other

All Publications (25 results)

[Publications] Kato, K., Usui, S.: "Logarithmic Hodge structures and their moduli"(preprint).
[Publications] Kato, K., Usui, S.: "Borel-Serre spaces and spaces of SL(2)-orbits"Advanced Studies in Pure Math.: Algebraic Geometry 2000, Azumino. (to appear).
[Publications] Usui, S.: "Recovery of vanishing cycles by log geometry"Tohoku Math. J. 53-1. 1-36 (2001)
[Publications] Kato, K.(with Matsubara, T., Nakayama, C.: "Log C^∞-functions and degenerations of Hodge structures"Advanced Studies in Pure Math.: Algebraic Geometry 2000, Azumino. (to appear).
[Publications] 向井茂: "Verlinde公式の幾何学"数理解析研究所講究録「組合せ論的表現論をめぐる話題,2000年10月」. (採用予定).
[Publications] Konno, K.: "On the quadric hull of a canonical surface"(preprint).
[Publications] Konno, K.(with Ashikaga, T.): "Local and global properties of pencils of algebraic curves"(prepribt).
[Publications] Konno, K.: "1-2-3 theorem for curves on algebraic surfaces"J. reine angew. Math.. 533. 171-205 (2001)
[Publications] Sato, E.(with Kachi, Y.): "Segre's reflexivity and an inductive characterization of hyperquadrics"Memoirs of A. M. S.. (2002)
[Publications] Mori, S.: "On a hyperplane section theorem of Gurjar"Math. Ann. 319. 533-537 (2001)
[Publications] Sumihiro, H.(with Tagami, S.): "A splitting theorem for rank two vector bundles on projective spaces in positive characteristic"Hiroshima Math. J. 31. 51-57 (2001)
[Publications] Saito, S.: "Infinitesimal logarithmic Torelli problem for degenerating hypersurfaces in P^n"Advanced Studies in Pure Math.:Algebraic Geometry 2000, Azumino. (to appear).
[Publications] Saito, S.: "Higher normal functions and Griffiths groups"J. of Algebraic Geometry. 11・1. 161-201 (2002)
[Publications] Nakamura, I.: "A compactification of the moduli scheme of abelian varieties"mathAG/0107158(e-print).
[Publications] Nakamura, I.: "Plane cubic curves-from Hesse to Mumford"Sugaku, 岩波書店. 53. 241-258 (2001)
[Publications] Nakamura, I.: "Hilbert schemes of abelian group orbits"J. Algebraic Geometry. 10. 757-779 (2001)
[Publications] Nakamura, I(with Terasoma, T.): "Moduli space of elliptic curves with Heisenberg level structure"Moduli of Abelian Varieties, Proc. of Texel conference 1999, Progress in Math., Birkhauser. 195. 299-324 (2001)
[Publications] Namikawa, Y.: "Counter-example to global Torelli problem for irreducible symplectic manifolds"(preprint).
[Publications] Namikawa, Y.: "A note on symplectic singularities"(preprint).
[Publications] Namikawa, Y.: "Projectivity criterion of Moishezon spaces and density of projective symplectic varieties"International J. Math. (to appear).
[Publications] Namikawa, Y.: "Deformation theory of Calabi-Yaus"Sugaku Exposition, A.M.S. (to appear).
[Publications] Namikawa, Y.: "Stratified local moduli of Calabi-Yau threefolds"Topology. (to appear).
[Publications] Namikawa, Y.: "Extension of 2-forms and symplectic varieties"J. Reine Angew. Math.. 539. 123-147 (2001)
[Publications] Namikawa, Y.: "Deformation theory of singular symplectic n-folds"Math. Ann. 319. 597-623 (2001)
[Publications] Namikawa, Y.: "Global smootyhing of Calabi-Yau threefolds II"Compositio Math.. 125. 55-68 (2001)

2001 Fiscal Year Annual Research Report

退化からみた代数幾何学・Hodge理論・Log幾何学相互の関係の研究

Principal Investigator

臼井 三平 大阪大学, 大学院・理学研究科, 教授 (90117002)

Research Products

[Publications] Kato, K., Usui, S.: "Logarithmic Hodge structures and their moduli"(preprint).

[Publications] Kato, K., Usui, S.: "Borel-Serre spaces and spaces of SL(2)-orbits"Advanced Studies in Pure Math.: Algebraic Geometry 2000, Azumino. (to appear).

[Publications] Usui, S.: "Recovery of vanishing cycles by log geometry"Tohoku Math. J. 53-1. 1-36 (2001)

[Publications] Kato, K.(with Matsubara, T., Nakayama, C.: "Log C^∞-functions and degenerations of Hodge structures"Advanced Studies in Pure Math.: Algebraic Geometry 2000, Azumino. (to appear).

[Publications] 向井茂: "Verlinde公式の幾何学"数理解析研究所講究録「組合せ論的表現論をめぐる話題,2000年10月」. (採用予定).

[Publications] Konno, K.: "On the quadric hull of a canonical surface"(preprint).

[Publications] Konno, K.(with Ashikaga, T.): "Local and global properties of pencils of algebraic curves"(prepribt).

[Publications] Konno, K.: "1-2-3 theorem for curves on algebraic surfaces"J. reine angew. Math.. 533. 171-205 (2001)

[Publications] Sato, E.(with Kachi, Y.): "Segre's reflexivity and an inductive characterization of hyperquadrics"Memoirs of A. M. S.. (2002)

[Publications] Mori, S.: "On a hyperplane section theorem of Gurjar"Math. Ann. 319. 533-537 (2001)

[Publications] Sumihiro, H.(with Tagami, S.): "A splitting theorem for rank two vector bundles on projective spaces in positive characteristic"Hiroshima Math. J. 31. 51-57 (2001)

[Publications] Saito, S.: "Infinitesimal logarithmic Torelli problem for degenerating hypersurfaces in P^n"Advanced Studies in Pure Math.:Algebraic Geometry 2000, Azumino. (to appear).

[Publications] Saito, S.: "Higher normal functions and Griffiths groups"J. of Algebraic Geometry. 11・1. 161-201 (2002)

[Publications] Nakamura, I.: "A compactification of the moduli scheme of abelian varieties"mathAG/0107158(e-print).

[Publications] Nakamura, I.: "Plane cubic curves-from Hesse to Mumford"Sugaku, 岩波書店. 53. 241-258 (2001)

[Publications] Nakamura, I.: "Hilbert schemes of abelian group orbits"J. Algebraic Geometry. 10. 757-779 (2001)

[Publications] Nakamura, I(with Terasoma, T.): "Moduli space of elliptic curves with Heisenberg level structure"Moduli of Abelian Varieties, Proc. of Texel conference 1999, Progress in Math., Birkhauser. 195. 299-324 (2001)

[Publications] Namikawa, Y.: "Counter-example to global Torelli problem for irreducible symplectic manifolds"(preprint).

[Publications] Namikawa, Y.: "A note on symplectic singularities"(preprint).

[Publications] Namikawa, Y.: "Projectivity criterion of Moishezon spaces and density of projective symplectic varieties"International J. Math. (to appear).

[Publications] Namikawa, Y.: "Deformation theory of Calabi-Yaus"Sugaku Exposition, A.M.S. (to appear).

[Publications] Namikawa, Y.: "Stratified local moduli of Calabi-Yau threefolds"Topology. (to appear).

[Publications] Namikawa, Y.: "Extension of 2-forms and symplectic varieties"J. Reine Angew. Math.. 539. 123-147 (2001)

[Publications] Namikawa, Y.: "Deformation theory of singular symplectic n-folds"Math. Ann. 319. 597-623 (2001)

[Publications] Namikawa, Y.: "Global smootyhing of Calabi-Yau threefolds II"Compositio Math.. 125. 55-68 (2001)

臼井三平大阪大学, 大学院・理学研究科, 教授 (90117002)