Various problems related to classifications around the higher dimensional birational geometry

与高维双有理几何分类相关的各种问题

基本信息

批准号：
09440010
负责人：
MORI Shigefumi
金额：
$ 6.02万
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：
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-09440010/
关键词：
minimal model abundance conjecture mirror conjecture K3 surface Calabi-Yau manifold Abelian variety B-model terminal singularity モーデル・ヴェイユ格子アパンダンス予想 A-モデル Chern数極小モデル理論 flip Mirror対称 Calabi-Yau多様体 Hilbert scheme special

项目摘要

Mori, together with Kollar, published an book on the birational geometry of algebraic varieties. Topics treated in the book include a simpler alternate definition of dlt singularity, a simpler proof of the rationality of dlt singularities and an alternate proof of the existence of the 3-dimensional stable flips.He also published a review of his work on the existence of rational curves on algebraic varieties, in which he posed problems on the refinement of the existence theorem, the generalization of the cone theorem, etc. Together with Kollar, Miyaoka and Takagi, he finished the proof of the boundedness of the terminal Q-Fano 3-folds, which will be published shortly. (The proof of Reid's conjecture on 3-dimensional flips in the reducible case is in preparation.)Miyaoka is preparing the proof for the assertion that every projective smooth n-fold with an external ray of length at least n+1 is isomorphic to the projective space, which is to be published soon.Nakayama has investigated prob … More lems related to the minimal model theory. He proved that small deformation of terminal singularities are terminal (in preparation). He also proved that, assuming the abundance conjecture, every nonsingular projective manifold whose universal covering is an affine space has an abelian variety as a finite etale covering.Mukai's work are on the algebraic construction of moduli spaces and various geometries on them, including certain duality of polarized K3 surfaces. He is also investigating the Verlinde formula on the moduli spaces of the parabolic vector bundles.Masahiko Saito, together with Hosono and Takahashi, has formulated a generalzation of the holomorphic anomaly equation on the counting of higher genus curves on rational elliptic surfaces and verified that it is consistent with the B-model computation in the case of genus 0,1.Hayakawa has proved that, for every 3-dimensional terminal singularity of index at least two, an arbitrary exceptional divisor with the minimal discrepancy can be obtained by an explicit "weighted blow-up".Dr. Kenji Matsuki at Purdue University was invited for two weeks from the end of June 1999 to present his recent work on the weak factorization of the birational map in a series of lectures (the lecture notes will be published. ) Less

Mori 与 Kollar 一起出版了一本关于代数簇的双有理几何的书，书中的主题包括 dlt 奇点的更简单的替代定义、所处理的 dlt 奇点的合理性的更简单的证明以及 3 存在的替代证明。他还发表了对代数簇有理曲线的存在性的研究的评论，其中提出了存在定理的细化、与Kollar、Miyaoka和Takagi一起完成了终端Q-Fano 3-folds有界性的证明，并将很快发表（Reid's conjecture on 3-Dimensional Flips in the Reducible）。案例正在准备中。）Miyaoka 正在准备证明以下断言：每个具有长度至少为 n+1 的外部射线的投影平滑 n 重与投影同构空间，即将出版。中山研究了与最小模型理论相关的问题，他证明了终端奇点的小变形是终端的（正在准备中）。他还证明了，假设丰度猜想，每个非奇点。其通用覆盖是仿射空间的射影流形具有作为有限 etale 覆盖的阿贝尔簇。Mukai 的工作是模空间及其上的各种几何的代数构造，包括某些他还在研究抛物线向量丛的模空间上的 Verlinde 公式。Masahiko Saito 与 Hosono 和 Takahashi 一起，提出了有理数上高等亏格曲线计数的全纯反常方程的推广。椭圆曲面并验证其与亏格 0,1 情况下的 B 模型计算一致。Hayakawa 证明了，对于每一个指数至少为2的3维终端奇异性，可以通过显式的“加权爆炸”获得具有最小差异的任意异常除数。从1999年6月下旬起，普渡大学的Kenji Matsuki博士受邀进行了两周的研究。在一系列讲座中展示他最近关于双有理映射的弱因式分解的工作（讲座笔记将被出版。） Less