Compact submanifold of the projective space and semismple algebraic group action
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Let $X$ be a compact submanifold of $mathbb CP^n$ such that there exists a semisimple complex linear algebraic group $G$ acts transitively on $X$. If $X$ is $G$-equivariantly embedded in $mathbb CP^n$. How to show that $X$ is a flag manifold?
differential-geometry algebraic-geometry lie-groups algebraic-groups
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up vote
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Let $X$ be a compact submanifold of $mathbb CP^n$ such that there exists a semisimple complex linear algebraic group $G$ acts transitively on $X$. If $X$ is $G$-equivariantly embedded in $mathbb CP^n$. How to show that $X$ is a flag manifold?
differential-geometry algebraic-geometry lie-groups algebraic-groups
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Let $X$ be a compact submanifold of $mathbb CP^n$ such that there exists a semisimple complex linear algebraic group $G$ acts transitively on $X$. If $X$ is $G$-equivariantly embedded in $mathbb CP^n$. How to show that $X$ is a flag manifold?
differential-geometry algebraic-geometry lie-groups algebraic-groups
Let $X$ be a compact submanifold of $mathbb CP^n$ such that there exists a semisimple complex linear algebraic group $G$ acts transitively on $X$. If $X$ is $G$-equivariantly embedded in $mathbb CP^n$. How to show that $X$ is a flag manifold?
differential-geometry algebraic-geometry lie-groups algebraic-groups
asked Aug 12 at 0:03
Ronald
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