Transversal study on Ultradiscretizing phenomena in algebraic geometry, learning theory and biological mathematics

代数几何、学习理论和生物数学中超离散现象的横向研究

• 批准号: 21540045
• 负责人: KOBAYASHI Masanori
• 金额: $ 2.83万
• 依托单位: Tokyo Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540045/
• 关键词: トロピカル幾何; 特異点; 代数幾何学; 工程計画問題; 代数学; トポロジー; 圏; K3曲面; 代数幾何; Z-アフィン幾何; 反射的多面体; 生体生命情報学; 運動量写像

(1) For the fourteen unimodal exceptional hypersurface singularities, we have constructed algebraic cycles in the derived category of K3 surfaces, and shown that we can recover the Dynkin diagrams from their categorical intersection numbers.(2) We have shown that the famous ninety-five families of weighted K3 hypersurfaces are, in fact, essentially seventy-five families by constructing concrete correspondences.(3) We introduced a geometric point of view to the scheduling problems for the first time, showed that the change of critical paths occurred at a tropical hypersurface and developed totally new method to visualize the transition of paths.(4) We did a topological classification of tropical elliptic curves.(5) We discussed about algebro-geometric method for acquiring abilities by neural networks.

(1) 对于 14 个单峰异常超曲面奇点，我们在 K3 曲面的派生类别中构造了代数环，并表明我们可以从它们的分类交集数中恢复 Dynkin 图。(2) 我们已经证明，著名的九十五族加权 K3 超曲面实际上本质上是七十五族，通过构造具体的 (3)我们首次引入了调度问题的几何观点，表明关键路径的变化发生在热带超曲面上，并开发了可视化路径转变的全新方法。(4)我们对热带椭圆曲线进行了拓扑分类。(5)我们讨论了通过神经网络获取能力的代数几何方法。

项目成果

A note on exceptional umimodal singularities and K3 surfaces

关于特殊的 umimodal 奇点和 K3 曲面的注释

• 发表时间: 2012
• 作者: Masanori Kobayashi;et al
• 通讯作者: et al

Isomorphism among families of weighted K3 hypersurfaces,Topology of singularities and related topics,the Institute of Mathematics

加权K3超曲面族间的同构，奇点拓扑及相关专题，数学研究所

• 发表时间: 2010
• 作者: Masanori Kobayashi;M.Mase;Hideto Asashiba;吉川謙一;Chikashi Miyazaki;M. Kobayashi
• 通讯作者: M. Kobayashi

Z-affine transformations and families of K3 hypersurfaces, 2011 NIMS Hot Topics Workshop on Computational Aspects of Birational Geometry

Z 仿射变换和 K3 超曲面族，2011 NIMS 双有理几何计算方面的热门主题研讨会

• 发表时间: 2011
• 作者: 亀山統胤;西田憲司;H. Ishida and H. Tokunaga;Miyazaki Chikashi;Izuru Mori;M. Kobayashi
• 通讯作者: M. Kobayashi

A not e on exceptional unimodal singularities and K3 surfaces

关于异常单峰奇点和 K3 曲面的注释

• 发表时间: 2012
• 作者: M. Kobayashi;M. Mase and K. Ueda
• 通讯作者: M. Mase and K. Ueda

Tropical Geometry of PERT

PERT 的热带几何

• 发表时间: 2011
• 作者: Masanori Kobayashi;et al;Terai Naoki and Trung Ngo Viet;Hideto Asashiba;T. Ashikaga and K.-I. Yoshikawa;西田憲司;Ogata Shoetsu;M. Kobayashi and S. Odagiri
• 通讯作者: M. Kobayashi and S. Odagiri