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

莫里（Mori）与Prokhorov共同提供了Iskovskikh的猜想，这是在3维端子Q-Conic束的基本表面的奇异点上，并将纤维分类为点。 Mukai明确描述了K3表面24的原始极化，并证明了模量和普遍家族的普遍性。 Namikawa明确描述了Mukai Flops的相干滑轮类别的等效性。他还移动了变形平滑度的等效性和用于投射复杂对称品种的毛茸茸的分辨率的存在。 Nakayama发表了关于代数品种分区的数值研究。他与藤本托（Fujimoto）共同确定了具有非内加kodaira尺寸的非单词射击的结构，并具有高度> 1的过滤性自我形态。川塔（Kawakita）发表了三维分区收缩的分类，该收缩收缩了分隔符于非戈伦斯坦点。他被证明是反向调整……更多用于对数概念性。 Oguiso与Hosono，Lian和Yau共同为复杂的投影K3表面的傅立叶Mukai对数提供了明确的公式。他还确定了作用在某些复杂K3表面的最大有限溶液组。高吉（Takagi）将主要的奇异范诺（Fano）归类为三倍，只有引用终端奇异性，可以满足抗典型系统上的一般大象的猜想。与Budur and Mustata共同给出了主体理想的B功能的组合公式，为任意理想定义了B功能，并证明了其与乘数思想的关系。 ABE研究了用固定确定的束的载体束的模量在基本曲线退化为淋巴结曲线时退化。 Hayakawa修订并证明了Reid对3维终极奇异性的经济爆炸的存在。海外合作研究员Matsuki成功修订了不变的，并在其项目中与Kawanoue在积极特征上降低了终止的猜想。较少的