Classification and structure of polarized varieties

极化品种的分类及结构

• 批准号: 09440008
• 负责人: FUJITA Takao
• 金额: $ 5.31万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09440008/
• 关键词: polarized varieties; adjoint bundle; Kodaira energy; 対数構造; 随伴線形系; adjoint fibration; 対数偏極多様体

The head investigator Fujita has classified non-singular polarized threefolds with Kodaira energy less than -1/2, and described precisely the structure of the adjoint fibrations. He further found out that the techniques of Kawachi-Masek in the study of base points of adjoint linear systems of normal polarized surfaces can be utilized also in the case of normal surfaces with Q-boundaries.Investigator Ishii has found a sufficient condition for minimal models of singularities of certain type to be obtained by a weighted blow up, and proved that nondegenerate hypersurface singularities have minimal, canonical and log-canonical models. She further found a counter example to a conjecture by Reid on a characterization of hypersurface rational singularities by weights, and showed the existence of simple elliptic singularies not of known type. She showed also various important properties of the set of possible values of the invariant - KィイD12ィエD1 of normal surface singularities.Investigator Tsu … More ji has established the theory of analytic Zariski decomposition, and constructed natural singular Hermitian metrics with positive curvature for line bundles. He applied this theory in the study of pluri-canonical systems of varities of general type and many problems including the abundance conjecture for minimal varieties of any dimensions.Investigator Mizumoto has showed that there are good Eisenstein liftings between certain spaces of (quasi)-automorphic forms. He further showed various properties of certain L-functions and non-regular Eisenstein series related to SL(2, Z).Investigator Nakayama has generalized classical theoris of etale cohomology to logarithmic structures. Further, he established basic theories of log geometry of complex analytic spaces, which was used to prove the degeneration of l-adic weight spectral sequences over arbitrary fields.Investigator Kobayashi has studied the behaviours of real algebraic varieties under blowing up, especially in case of embedded curves in real plane. He also constructed an explicit example of a Calabi-Yau threefold with certain elliptic fibration whose set of real points is a SUSY 3-torus. Less

首席研究员Fujita将科代拉能量小于-1/2的非奇异偏振三重分类，并精确描述了伴随纤维化的结构。他进一步发现，Kawachi-Masek在研究正常极化曲面的伴随线性系统的基点时的技巧也可以用于具有Q-边界的正常曲面的情况。研究者石井找到了通过加权爆破获得某种类型的奇点的极小模型的充分条件，并证明了非退化超曲面奇点具有极小，典型和对数典型模型。她进一步发现了一个反例，以猜想里德的一个特点，超曲面理性奇点的重量，并表明存在简单的椭圆奇点不知道的类型。她还展示了各种重要的属性的一套可能的价值观的不变量- K D12 D1的正常表面奇点。研究员大津 ...更多信息 Ji建立了解析Zebraki分解理论，并构造了线丛的具有正曲率的自然奇异Hermitian度量。他应用这一理论在研究多典型系统的变种的一般类型和许多问题，包括丰富的猜想最小品种的任何dimensions.Investigator水元已表明，有良好的爱森斯坦提升之间的某些空间的（准）自守形式。他进一步证明了与SL（2，Z）有关的某些L-函数和非正则Eisenstein级数的各种性质。研究员小林研究了真实的代数簇在爆破下的行为，特别是在真实的平面上嵌入曲线的情况下。他还建造了一个明确的例子卡-丘三倍与某些椭圆纤维化的一套真实的点是一个超对称3环面。少

项目成果

S. Mizumoto: "Certain L - functions at S=1/2"Acta Arithmetica. 88. 51-66 (1999)

S. Mizumoto：“某些 L - 在 S=1/2 处起作用”《算术学报》。

M. Kobayashi and T. C. Kuo: "On blow-analytic equivalence of embedded curve singularities, in Real analytic and algebraic singularities (T. Fukuda et al. eds.)"Pitman Research Notes in Math. Series 381. 30-37 (1998)

M. Kobayashi 和 T. C. Kuo：“实数解析和代数奇点中嵌入曲线奇点的吹分析等价性（T. Fukuda 等人编辑）”Pitman Math 研究笔记。

K. Kato and C. Nakayama: "Log Betti cohomoloty, log etale cohomology, and log de Rham cohomology of log schemes over C"Kodai Math. J.. 22. 161-186 (1999)

K. Kato 和 C. Nakayama：“C 上对数方案的 Log Betti 上同调、log etale 上同调和 log de Rham 上同调”Kodai Math。

MIZUMOTO Shin-ichiro: "Certain L-functions at S=1/2"Acta Arithmetica. 88. 51-66 (1999)

水本信一郎：“S=1/2 时的某些 L 函数”《算术学报》。

M.Somekawa: "Log-syntomc regulators and p-adic polylogurichm" K-theory. 361. 1-29 (1998)

M.Somekawa：“对数符号调节器和 p-adic 多语言”K 理论。