Fixed locus of $Ab(Y)$ and subtorus
Let $Y$ be a compact Kähler manifold of dimension $n$ and an action of $S_3$
on $Y$ is a homomorphism from $S_3$ to the group Homeo$(Y)$ of all homeomorphisms from $Y$ to itself.
Now there is an $S_3$ action on Alb($Y$):=$H^{n-1,n}(X)/im(H^{2n-1}(X,mathbb{Z}))$, induced by the action on $Y$. Let $X$ be the fixed locus of Alb($Y$) by this $S_3$ action. Then why is $X$ a
subtorus?
algebraic-geometry algebraic-topology kahler-manifolds
asked Jan 4 at 16:26
66666666
1,270620
add a comment |
Let $Y$ be a compact Kähler manifold of dimension $n$ and an action of $S_3$
on $Y$ is a homomorphism from $S_3$ to the group Homeo$(Y)$ of all homeomorphisms from $Y$ to itself.
Now there is an $S_3$ action on Alb($Y$):=$H^{n-1,n}(X)/im(H^{2n-1}(X,mathbb{Z}))$, induced by the action on $Y$. Let $X$ be the fixed locus of Alb($Y$) by this $S_3$ action. Then why is $X$ a
subtorus?
algebraic-geometry algebraic-topology kahler-manifolds
asked Jan 4 at 16:26
66666666
1,270620
3
If $Y$ is just a topological space, what is $Alb(Y)$?
– Sasha
Jan 4 at 16:51
@Sasha I have fixed.
– 6666
Jan 5 at 0:58
add a comment |
Let $Y$ be a compact Kähler manifold of dimension $n$ and an action of $S_3$
on $Y$ is a homomorphism from $S_3$ to the group Homeo$(Y)$ of all homeomorphisms from $Y$ to itself.
Now there is an $S_3$ action on Alb($Y$):=$H^{n-1,n}(X)/im(H^{2n-1}(X,mathbb{Z}))$, induced by the action on $Y$. Let $X$ be the fixed locus of Alb($Y$) by this $S_3$ action. Then why is $X$ a
subtorus?
algebraic-geometry algebraic-topology kahler-manifolds
asked Jan 4 at 16:26
66666666
1,270620
Let $Y$ be a compact Kähler manifold of dimension $n$ and an action of $S_3$
on $Y$ is a homomorphism from $S_3$ to the group Homeo$(Y)$ of all homeomorphisms from $Y$ to itself.
Now there is an $S_3$ action on Alb($Y$):=$H^{n-1,n}(X)/im(H^{2n-1}(X,mathbb{Z}))$, induced by the action on $Y$. Let $X$ be the fixed locus of Alb($Y$) by this $S_3$ action. Then why is $X$ a
subtorus?
algebraic-geometry algebraic-topology kahler-manifolds
algebraic-geometry algebraic-topology kahler-manifolds
asked Jan 4 at 16:26
66666666
1,270620
asked Jan 4 at 16:26
66666666
1,270620
edited Jan 5 at 1:23
6666
asked Jan 4 at 16:26
66666666
1,270620
asked Jan 4 at 16:26
66666666
1,270620
asked Jan 4 at 16:26
66666666
1,270620
1,270620
3
If $Y$ is just a topological space, what is $Alb(Y)$?
– Sasha
Jan 4 at 16:51
@Sasha I have fixed.
– 6666
Jan 5 at 0:58
add a comment |
3
If $Y$ is just a topological space, what is $Alb(Y)$?
– Sasha
Jan 4 at 16:51
@Sasha I have fixed.
– 6666
Jan 5 at 0:58
3
3
If $Y$ is just a topological space, what is $Alb(Y)$?
– Sasha
Jan 4 at 16:51
If $Y$ is just a topological space, what is $Alb(Y)$?
– Sasha
Jan 4 at 16:51
@Sasha I have fixed.
– 6666
Jan 5 at 0:58
@Sasha I have fixed.
– 6666
Jan 5 at 0:58
add a comment |
0
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3
If $Y$ is just a topological space, what is $Alb(Y)$?
– Sasha
Jan 4 at 16:51
@Sasha I have fixed.
– 6666
Jan 5 at 0:58