Studies of families of rational curves and characterizations of homogeneous manifolds

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。

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.