有理齐性空间切面的一些几何性质 献给杨乐教授80华诞

Some geometrical properties of linear sections of rational homogeneous spaces

有理齐性空间是最简单的射影代数簇,而对它的研究与刻画一直是代数几何的热点问题与灵感来源.有理齐性空间的切面则提供了大量有趣的代数簇的例子,而对它的系统研究才刚刚起步.本文拟从以下几个方面概述最近在此方向上的进展:自同构群与拟齐性、向量群的等变紧化和形变刚性.

Rational homogeneous spaces are among the simplest algebraic varieties,the study and characteri zation of which is one of the key problems and sources of inspiration in algebraic geometry.Linear sections of rational homogeneous varieties provide many interesting examples of algebraic varieties,a systematic study of which is just beginning.We report recent progress on this subject from the following perspectives:automorphism groups and quasi-homogeneity,equivariant compactifications of vector groups,deformation rigidity.