Self-dual Projective Algebraic Varieties Associated With Symmetric Spaces
Self-dual Projective Algebraic Varieties Associated With Symmetric Spaces
复制标题
与对称空间相关的自对偶射影代数簇
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
E. Tevelev
中科院分区：
文献类型：
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作者：
V. Popov;E. Tevelev
发现了一类投射自对偶代数簇。也就是说，我们考虑复对称空间的各向同性群在各向同性模的投影化幂零簇上的作用。对于它们，我们对所有轨道闭包X进行分类，使得（X = overset{lower0.5emhbox{$smash{scriptscriptstylesmile}$}}{X}），其中（overset{lower0.5emhbox{$smash{scriptscriptstylesmile}$}}{X}）是X的射影对偶。对于所考虑的轨道闭包，我们给出了射影自对偶的代数准则。
We discover a class of projective self-dual algebraic varieties. Namely, we consider actions of isotropy groups of complex symmetric spaces on the projectivized nilpotent varieties of isotropy modules. For them, we classify all orbit closures X such that (X = overset{lower0.5emhbox{$smash{scriptscriptstylesmile}$}}{X} ) where (overset{lower0.5emhbox{$smash{scriptscriptstylesmile}$}}{X} ) is the projective dual of X. We give algebraic criteria of projective self-duality for the considered orbit closures.