Various Problems on the Classification in Higher Dimensional Birational Geometry

Mori与Prokhorov在三维末端q -圆锥束基面上的奇异点上证明了Iskovskikh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 flops相干束派生范畴的等价性。他还提出了投影复辛变异体的变形光滑性的等价性和渐变分辨率的存在性。Nakayama发表了关于代数变量的除数的数值研究。他与Fujimoto共同确定了一个具有非负Kodaira维的非奇异射影3-fold的结构，该3-fold具有>1次的满射自态射。Kawakita发表了将一个除数压缩到一个非gorenstein点的三维除数收缩的分类。他证明了逆附加…更多关于对数正则性。Oguiso与Hosono， Lian和Yau一起给出了复射影K3曲面的傅里叶Mukai对数目的显式公式。他还确定了作用于某些复杂K3表面的最大有限可解群。Takagi对反正则系统上只有商端点奇点满足一般大象猜想的原始奇异Fano三叠进行了分类。Saito与Budur和Mustata共同给出了一个关于主理想的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研究了当基曲线退化为节点曲线时，具有固定行列式束的向量束的模如何退化。早川修正并证明了里德关于三维终端奇点经济爆炸存在的猜想。国外合作研究者Matsuki在与Kawanoue合作的项目中，成功地修正了不变量，并绕过了终止猜想。少

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