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seen Feb 27 '13 at 5:05

Feb
13
comment Lifting an automorphism to the universal covering space..
Thanks for clarifying the point.
Feb
10
comment Automorphism of the function field and birational map
Thank you for providing me with the reference, Martin.
Feb
10
comment Lifting an automorphism to the universal covering space..
I may misunderstand something. We are interested in the case $Z=X$ and $f \in \mathrm{Aut}(X)$. To me the condition looks like $\pi_1(X) \le p_*(\pi_1(Y))=\{0\}$.
Feb
9
comment Lifting an automorphism to the universal covering space..
Isn't $p_{*}(\pi_{1}(Y))$ trivial in your answer?
Feb
5
comment Chern classes of free quotient manoflds
>Jason Thank you for pointing the error. Yes, I need to assume holomorphicity of the action.
Feb
4
comment Chern classes of free quotient manoflds
Yes, but that does not give us much information except for the top class.
Feb
4
comment A question on Hermitian metric on complex manifold.
Daniel, thank you for the detailed answer. This makes my understanding clearer.
Jan
7
comment About twistor space of a K3 surface
Opps! You are right. Let me think for a bit.
Jan
5
comment Arithmetic and geometric genus
Thank you for the comment.
Jan
1
comment Holonomy group of quotient manifold
Without any condition, they must be different. For example the fundamental group of a manifold affect its holonomy group.
Dec
29
comment Understanding induced representations
Thank you for the answer, anon. I am now convinced by your "the 'most free' representation of G" argument. I really like the way you think about it. Fortunately I have two good answers but unfortunately cannot "accept" two answers. So please let me choose Paul's answer as he posts it earlier.
Dec
29
comment Understanding induced representations
Thank you for the answer, Paul. It makes my understanding much clearer and better.
Dec
29
comment Understanding induced representations
It is not as clear as the restriction of representation. In my opinion, there are many "induced" representation in contrast to restriction, which is obviously unique. "The" induced representation should be canonical in some sense; I think people call $Ind_H^G(\phi)$ "the induced representation" because of the Frobenius reciprocity. But now I don't see why your definition gives rise to such a duality. This is one of the reasons why I feel uneasy with it.
Dec
27
comment Existence of a square root of a given line bundle via Chern class?
You are right. I usually work in algebraic or holomorphic category and am being confused. Thanks.
Dec
27
comment Existence of a square root of a given line bundle via Chern class?
I think that complex line bundles are classified by elements in $H^1(M,\mathcal{O}^{\times})$ and the first Chern class is the image of the boundary map of the exponential exact sequence $0\rightarrow \mathbb{Z}\rightarrow \mathcal{O} \rightarrow \mathcal{O}^{\times} \rightarrow 0$. I am not sure if this map is injective and first Chern classes really classifies complex line bundles.
Dec
27
comment $A = B^2$ for which matrix $A$?
Thanks for the answer, Bryce. I will take a look at the Cholesky decomposition.
Dec
15
comment Elliptic equation and barrier estimate.
I now see your argument. Weakly minimum principle implies $x_0$ is the minimum of $w$ on $\overline{U}$.
Dec
15
comment Elliptic equation and barrier estimate.
Yes, $\partial U$ is a contour of $u$, so $\nabla u(x_0)$ is parallel to $\nu(x_0)$.
Dec
15
comment Elliptic equation and barrier estimate.
Sorry for annoying question, but I still don't see why $u$ and $w$ attains local minima at $x_0$. Assuming this fact, your argument makes a perfect sense.
Dec
14
comment Moduli space of elliptic curves with $C_n$ action
I forgot to say an important point; my $C_n$-action is always translation. Thank you all for comments clarifying ambiguous points.