Studies of families of rational curves and characterizations of homogeneous manifolds

有理曲线族的研究和齐次流形的表征

• 批准号: 24840008
• 负责人: WATANABE Kiwamu
• 金额: $ 1.91万
• 依托单位: Saitama University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Research Activity Start-up
• 财政年份: 2012
• 资助国家: 日本
• 起止时间: 2012-08-31 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-24840008/
• 关键词: ファノ多様体; ネフ接束; 等質多様体; ネフな接束; 有理曲線

I have studied Fano manifolds with nef tangent bundles. It is conjectured that such manifolds are rational and homogeneous by Campana and Peternell, which is called the CP conjecture. First, I proved that the conjecture holds for Fano 5-folds of Picard number >1. The result was published from Math Zeitsherift. On the other hand, I studied some problems related to the CP conjecture with R. Munoz, G. Occhetta, L. Sola Conde and J. Wiśniewski. In particular, we proved that Fano manifolds whose elementary contractions are smooth P1-fibrations are complete flag manifolds. As a corollary, the CP conjecture can be boiled down to another problem. We wrote two papers on this topic and these papers are submitted.

我研究了具有Nef切丛的Fano流形。Campana和Peternell猜想这种流形是有理齐次的，称为CP猜想。首先，我证明了这个猜想对五倍Picard数&gt；1成立。这一结果发表在《数学时代》杂志上。另一方面，我与R.Munoz，G.Occhetta，L.Sola Conde和J.WiśNiewski研究了与CP猜想有关的一些问题。特别地，我们证明了初等压缩是光滑的P_1-贝塔的Fano流形是完备的旗形。作为推论，CP猜想可以归结为另一个问题。我们就这个主题写了两篇论文，并提交了这些论文。

项目成果

Smooth P1-fibrations and Campana-Peternell conjecture

平滑 P1 纤维和 Campana-Peternell 猜想

• 发表时间: 2012
• 作者: 増田亮二;高橋陽太郎;金子良夫，十倉好紀;西岡斉治;渡邉究
• 通讯作者: 渡邉究

Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle

• DOI: 10.1007/s00208-014-1083-x
• 发表时间: 2015-04-01
• 期刊: MATHEMATISCHE ANNALEN
• 影响因子: 1.4
• 作者: Munoz, Roberto;Occhetta, Gianluca;Watanabe, Kiwamu
• 通讯作者: Watanabe, Kiwamu

Fano 5-folds with nef tangent bundles and Picard numbers greater than one

Fano 5 重，nef 切线丛且皮卡德数大于 1

• DOI: 10.1007/s00209-013-1185-2
• 发表时间: 2014
• 期刊: Math. Z.
• 作者: Paolo Cascini;Yoshinori Gongyo;丹下基生;K Watanabe
• 通讯作者: K Watanabe

Characterization of complete flag manifolds and Campana-Peternell conjecture

完整旗形流形的表征和 Campana-Peternell 猜想

• 发表时间: 2014
• 作者: 渡辺信三;重川一郎 (他;中島誠);Yoshinori Gongyo;宮崎彬，山崎高幸，末原大幹，難波俊雄 浅井祥仁，小林富雄，斎藤晴雄， 立松芳典，小川勇，出原敏孝;渡邉究
• 通讯作者: 渡邉究

完全旗多様体の特徴付けとCampana-Peternell予想

完整旗形流形的表征和 Campana-Peternell 猜想

• 发表时间: 2014
• 作者: Schenker M. A;Robertson B. E;Ellis R. S;Ono Y;McLure R. J;Dunlop J. S;Koekemoer A;Bowler R. A. A;Ouchi M;Curtis-Lake E;Rogers A. B;Schneider E;Charlot S;Stark D. P;Furlanetto S. R;and Cirasuolo M;渡邉究
• 通讯作者: 渡邉究