Homogeneous varieties for Hilbert schemes

Absolute Chow-Kuenneth decomposition for rational homogeneous bundles and for log homogeneous varieties

In this paper, we investigate Murre's conjecture on the existence of a Chow--Kuenneth decomposition for a rational homogeneous bundle $Z\to S$ over a smooth variety, defined over complex numbers. Chow-Künneth decomposition is exhibited for $Z$ whenever $S$ has a Chow--Kuenneth decomposition. The same conclusion holds for a class of log homogeneous varieties, studied by M. Brion.

代数簇的希尔伯特性质

Hilbert properties of varieties

本文综述了代数簇的希尔伯特性质及其变种的相关研究成果。

三元多项式簇上的同质局部nilpotent导出

Homogeneous locally nilpotent derivations on trinomial varieties

研究三元多项式簇的正则函数代数最细分级下的同质局部nilpotent导出的显式描述。

On the collapsing of homogeneous bundles in arbitrary characteristic

We study the geometry of equivariant, proper maps from homogeneous bundles $G\times_P V$ over flag varieties $G/P$ to representations of $G$, called collapsing maps. Kempf showed that, provided the bundle is completely reducible, the image $G\cdot V$ of a collapsing map has rational singularities in characteristic zero. We extend this result to positive characteristic and show that for the analogous bundles the saturation $G\cdot V$ is strongly $F$-regular if its coordinate ring has a good filtration. We further show that in this case the images of collapsing maps of homogeneous bundles restri…