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 共同证明了 Iskovskikh 关于 3 维终端 Q 圆锥束基面奇点的猜想，并在这些点上对纤维进行了分类，明确描述了具有 24 度原始偏振的 K3 表面，并且证明了模数和万有族的非理性，并明确地描述了 Mukai flop 的相干滑轮的派生范畴的等价性。射影复辛簇的变形平滑性和渐近解的存在性 Nakayama 与 Fujimoto 联合发表了关于代数簇除数的数值研究，确定了具有非负 Kodaira 维数和满射的非奇射影 3 重结构。 Kawakita 发表了将除数收缩为非 Gorenstein 的 3 维除数收缩的分类。他与 Hosono、Lian 和 Yau 一起证明了对数正则性的逆附加，给出了复射影 K3 曲面的傅里叶 Mukai 对数的显式公式。他还确定了最大有限可解群。作用于一些复杂的 K3 表面上，高木将初奇异性 Fano 分类为三重，只有商终端奇异性满足反正则系统上的一般大象猜想。 Saito 与 Budur 和 Mustata 一起给出了主理想 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 研究了固定向量丛的模。当基曲线退化为节点曲线时，行列束退化，修正并证明了 Reid 关于 3 维终端奇点经济爆炸的存在性的猜想。研究员 Matsuki 在他与 Kawanoue 合作的项目中成功修正了不变量并双关了终止猜想，以实现积极特征的去奇异化。