Research on T-duality of Calabi-Yau manifolds of dimension less than or equal to four

小于等于四维的Calabi-Yau流形的T对偶性研究

• 批准号: 16540031
• 负责人: KOBAYASHI Masanori
• 金额: $ 0.7万
• 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: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540031/
• 关键词: derived category; Calabi-Yau manifold; dulaity; learning; algebraic geometry; 代数幾何学; カラビ-ヤウ多様体; 超弦理論; 特異点; 計算論的学習理論

I have studied mainly on the relationship between Calabi-Yau manifolds and derived categories. In particular, we studied how one can recover a complex manifold from its derived category e.g. by defining stability condition, and what should be expected on the equivalence among derived categories of complex symplectic manifolds.I visited Okayama University on behalf of the annual autumn meeting of the Mathematical Society of Japan from September 19 to 23 and made exchanges of information to researchers of algebraic geometry, differential geometry and mathematical physics. I exchanged information at Kinosaki conference hail from October 24 to 28, mainly from the viewpoint of algebraic geometry.I organized an international workshop with Professor Daisuke Matsushita at Hokkaido University from November 21 to 25 on the research subject.There was a meeting on recent development of relating subjects on February 16 and 17. I have sent my graduate students to collect information on behalf of me and had a report from them.In relation to computational learning, I received a prize from The Japanese Society for Artificial Intelligence for the study on Newton diagrams with Professor Akio Yamamoto in Kyoto University and Professor Hiro-o Tokunaga in Tokyo Metropolitan University last year. We continued a study on noetherian rings.I bought relating magazines.

主要研究了Calabi-Yau流形与导范畴之间的关系。特别是，我们研究了如何通过定义稳定性条件等方法从复流形的导出范畴中恢复复流形，以及在复辛流形的导出范畴之间的等价性上应该期待什么。我于9月19日至23日代表日本数学学会秋季年会访问了冈山大学，并与代数几何的研究人员进行了信息交流。微分几何和数学物理。10月24日至28日，在城崎会议上，主要从代数几何的观点进行了信息交流。11月21日至25日，在北海道大学与松下大辅教授就该研究课题组织了国际研讨会。2月16日至17日，举行了相关课题最新进展的会议。在计算学习方面，我与京都大学的山本昭夫教授和首都大学的德永博雄教授一起，在牛顿图的研究上，去年获得了日本人工智能学会的奖项。我们继续研究诺特环，我买了相关的杂志。

项目成果

多項式のイデアルと正データからの学習

从多项式理想和正数据中学习

• 发表时间: 2005
• 期刊: 2005年情報論的学習理論ワークショップ予稿集
• 作者: 小林正典;徳永浩雄;山本章博
• 通讯作者: 山本章博

Identification of Newton diagram in the limit and resolution of singularities on complex hypersurface

复杂超曲面奇点极限和解析中牛顿图的辨识

• 发表时间: 2005
• 期刊: The Japanese society for Artificial Intelligence(in Japanese) SIG-FPAI-A403
• 作者: Masanori Kobayashi;Hiro-o Tokunaga;Akihiro Yamamoto
• 通讯作者: Akihiro Yamamoto

Ideals of polynomial rings and learning from positive data (in Japanese)

多项式环的理想和从正数据中学习（日语）

• 发表时间: 2005
• 期刊: Proc.of Eighth Workshop on Information-based Induction Science
• 作者: Masanori Kobayashi;Hiro-o Tokunaga;Akihiro Yamamoto
• 通讯作者: Akihiro Yamamoto

ニュートン図形の極限同定と複素超曲面の特異点解消.

牛顿图形的极限识别和复杂超曲面的奇点分辨率。

• 发表时间: 2005
• 期刊: 人工知能基本問題研究会資料SIG-FPAI-A403(2005)
• 作者: 小林正典;徳永浩雄;山本章博
• 通讯作者: 山本章博