权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

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和Kollar一起出版了一本关于代数簇的二元几何的书。这本书讨论的主题包括DLT奇点的一个更简单的另一种定义，DLT奇点的合理性的一个更简单的证明以及三维稳定反转存在的另一种证明。他还发表了一篇关于代数簇上有理曲线存在性的工作综述，其中他提出了存在定理的精化、锥定理的推广等问题。他与Kollar、Miyaoka和Takagi一起完成了终端q-Fano 3-折叠的有界性的证明，不久将出版。(关于可约情形下三维翻转的Reid猜想的证明正在准备中。)Miyaoka正在为以下断言准备证明：每个至少有n+1条外部射线的射影光滑n重与射影空间同构，这一结论即将发表。Nakayama已经研究了问题…更多的引理与极小模型理论有关。他证明了终端奇点的小变形是终端(在准备中)。他还证明了，在丰度猜想的假设下，每一个泛覆盖为仿射空间的非奇异射影流形都有一个作为有限元覆盖的交换簇.Mukai的工作是关于模空间及其上的各种几何的代数构造，包括极化K3曲面的某些对偶.他还研究了抛物向量丛的模空间上的Verlinde公式。齐藤雅彦与Hosono和Takahashi一起，建立了有理椭圆曲面上高亏格曲线计数的全纯反常方程的推广，并证明了它与亏格为0，1的情况下的B-模型计算是一致的。Hayakawa证明了，对于指数至少为2的三维终端奇点，可以通过显式的“加权爆破”来获得具有最小偏差的任意例外因子。普渡大学的松木健二应邀从1999年6月底开始为期两周，在一系列讲座中介绍他最近关于二元映射的弱因式分解的工作(讲座讲稿将出版)。)较少