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Various Problems on the Classification in Higher Dimensional Birational Geometry

高维双有理几何分类中的各种问题

基本信息

批准号：
16340004
负责人：
MORI Shigefumi
金额：
$ 5.89万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2007
项目状态：
已结题

项目摘要

Mori, jointly with Prokhorov, proved Iskovskikh's conjecture on the singular points of the base surface of a 3-dimensional terminal Q-conic bundle, and classified the fibers over the points. Mukai explicitly described the K3 surfaces with primitive polarization of degree 24, and proved the unirationality of the moduli and universal family. Namikawa explicitly described the equivalence of the derived categories of coherent sheaves for Mukai flops. He also moved the equivalence of deformation smoothability and existence of a crepent resolution for projective complex symplectic varieties. Nakayama published the numerical study on divisors of algebraic varieties. Jointly with Fujimoto, he determined the structure of a nonsingular projective 3-fold with non-negaive Kodaira dimension and with a surjective self morphism of degree >1. Kawakita published the classification of 3-dimensional divisorial contractions contracting a divisor to a non-Gorenstein point. He proved the inverse adjunction … More for log canonicity. Oguiso, jointly with Hosono, Lian and Yau, gave an explicit formula for the number of the Fourier Mukai pairs for a complex projective K3 surface. He else determined the maximal finite solvable group acting on some complex K3 surface. Takagi classified the primary singular Fano threefolds with only quotient terminal singularities satisfying General Elephant Conjecture on anti-canonical systems. Saito, jointly with Budur and Mustata, gave a combinatorial formula on the b-function of a principal ideal, defined the b-function for an arbitrary ideal, and proved its relation with multiplier ideals. Abe studied how the moduli of vector bundles with fixed determinant bundle degenerates when the base curve degenerates to a nodal curve. Hayakawa revised and proved Reid's conjecture on the existence of an economical blowup of a 3-dimensional terminal singularity. The overseas cooperative researcher Matsuki successfully revised the invariant and bipassed the termination conjecture in his project with Kawanoue toward desingularization in positive characteristics. Less

Mori与Prokhorov一起证明了Iskovskikh关于三维终端Q-锥丛基面奇点的猜想，并对点上的纤维进行了分类。Mukai明确地描述了具有24次原始极化的K3曲面，并证明了模和泛族的唯一性。Namikawa明确地描述了Mukai触发器的相干层的导出范畴的等价性。他还提出了等价的变形平滑性和存在的credential决议的投影复杂辛品种。中山发表了数值研究因子的代数簇。与藤本一起，他确定了一个非奇异射影3倍的结构，它具有非负的科代拉维数和一个满射自态度>1。Kawakita发表了分类的三维divisorial收缩收缩收缩一个除数到一个非Gorenstein点。他证明了逆加法 ...更多信息日志规范。Oguiso与Hosono、Lian和Yau共同给出了复射影K3曲面的Fourier Mukai对的数目的显式公式。他还确定了最大有限可解群作用于一些复杂的K3曲面。Takagi将反正则系统中只有商终端奇异点满足广义Elephant猜想的准奇异Fano三重分类。Saito与Budur和Mustata一起给出了关于主理想的b-函数的组合公式，定义了任意理想的b-函数，并证明了它与乘子理想的关系。Abe研究了行列式丛固定的向量丛的模在基曲线退化为节曲线时如何退化。Hayakawa修正并证明了Reid关于三维终端奇点存在经济爆破的猜想。海外合作研究员Matsuki在与Kawanoue合作的项目中成功地修正了不变量，并通过了终止猜想，以实现正特征的去奇异化。少

项目成果

期刊论文数量（277）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Poisson deformations and symplectic varieties

泊松变形和辛簇

DOI：
发表时间：
2009
期刊：
影响因子：
0
作者：
通讯作者：

Hilbert's 14th problem and Verlinde type formulas for rings of invariant polynomials

希尔伯特第 14 个问题和不变多项式环的 Verlinde 型公式

DOI：
发表时间：
2007
期刊：
影响因子：
0
作者：
S. Mukai;H. Nasu;S.Mukai;Shigeru Mukai;S. Mukai;S. Mukai;S. Mukai;Shigeru Mukai;S. Mukai;S. Mukai;S. Mukai;Shigeru Mukai
通讯作者：
Shigeru Mukai

Bimeromorphic automorphism groups of non-projective hyperkahler manifolds-a note inspired by C. T. McMullen

非射影超卡勒流形的双同构自同构群——受 C. T. McMullen 启发的注释