All Questions
Tagged with symmetric-spaces complex-geometry
10 questions
2
votes
1
answer
294
views
Complex quadric as a symmetric space
It is known that a smooth complex quadric is a symmetric space. For example, it is
$$\operatorname{Spin}(n+2)/G$$
where $G$ is the maximal parabolic subgroup.
I want a reference for more details and ...
- 21
0
votes
0
answers
75
views
General fiber and the symmetric product of an ample hypersurface
Let $Sym^m(X)$ be the $m$th symmetric product of a smooth projective variety $X$, $n=\dim(X)$, $Y_1$ an ample hypersurface of $X$, and $CH_0(X)_{hom}$ the Chow groups of $0$-cycles of degree $0$....
- 519
2
votes
1
answer
167
views
Automorphism group of Hermitian symmetric spaces
For a hermitian symmetric space $M$ one has its group of biholomorphic maps $\operatorname{Hol}(M)$ and its group of Riemannian isometries $\operatorname{Isom}(M)$. According to Prop. 1.6 of Milne - ...
- 10.4k
6
votes
1
answer
287
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Bounded non-symmetric domains covering a compact manifold
This question is somewhat related to this other question of mine.
I was wondering which are the known examples of bounded domains $\Omega$ in $\mathbb C^n$ admitting a compact free quotient.
By a ...
- 7,902
3
votes
0
answers
94
views
Isotropy symmetric holomorphic functions
Let $G$ be a bounded homogeneous domain in $\mathbb{C}^{n}$ and let $z\in G$.
Assume that $f$ is a holomorphic function on $G$, which is isotropy symmetric, i.e. $f\circ \varphi=f$ for any ...
- 5,529
3
votes
0
answers
90
views
Two questions on homogeneous domains
Let $G$ be a domain in $\mathbb{C}^{n}$ and let $Aut(G)$ be the group of biholomorphic selfmaps of $G$. $G$ is called:
(1) homogeneous if $Aut(G)$ acts transitively on $G$, i.e. for any $z,w\in G$ ...
- 5,529
3
votes
1
answer
266
views
Are harmonic maps quasiconformal at the boundary of hyperbolic spaces?
Let $M$ be a hyperbolic $3$-manifold and $X$ a negatively curved, simply connected space with geometric boundary $\partial X$.
If $\rho:\pi_1M\rightarrow Isom(X)$ does not fix a point in $\partial X$,...
- 10.4k
1
vote
0
answers
186
views
Ricci-flat Kähler metrics on symmetric varieties
Hallo,
I have a question on a paper of Azad and Kobayashi "Ricci-flat Kähler metrics on symmetric varieties". Here is the link: http://www.academia.edu/2579043/Ricci-...
- 53
5
votes
1
answer
680
views
Is the Baily--Borel compactification functorial?
The following question seems pretty natural, but searching online
and looking in some obvious places didn't turn up much, so maybe
I can ask it here. (Disclaimer: I'm a newcomer to this topic, so
...
user5117
11
votes
4
answers
2k
views
Hermitian symmetric spaces vs Hermitian homogeneous spaces
A Hermitian symmetric space is a connected complex manifold with a hermitian metric on which the group of holomorphic isometries acts transitively, and which satisfies the following extra condition: ...
- 2,713