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seen Apr 16 at 16:47

Mar
18
comment How can I prove that $\mathcal{O}_X(-n-1) \simeq \Lambda^n(T_X)^*$?
$\mathcal{O}_X(-n-1)$ only makes sense when $X$ is projective variety, and it also depends on an embedding of $X$ into projective space. Also, in general it's not true. It's only true for the special case $X = \mathbb{P}^n$. To see it, as @EricO.Korman says, you can consider Euler sequence.
Mar
18
comment Liouville's theorem for functions not bounded on an isolated set
What do you mean by "bounded on whole plane except for isolated set of points"? You mean that there exists a discrete subset $D \subseteq \mathbb{C}$ such that your function $f: \mathbb{C} - D \to \mathbb{C}$ is bounded?
Mar
17
revised Partial fraction expansion of $\frac{1}{x(x+1)(x+2)\cdots(x+n)}$
more elementary deriviation
Mar
17
answered Prove the determinant map is a natural transformation
Mar
17
answered Partial fraction expansion of $\frac{1}{x(x+1)(x+2)\cdots(x+n)}$
Mar
11
revised If $A^TA$ is invertible, then $A$'s columns are linearly independent (not necessarily square matrix)
added 84 characters in body
Mar
11
answered If $A^TA$ is invertible, then $A$'s columns are linearly independent (not necessarily square matrix)
Mar
11
answered Nonconstructible Algebraic Numbers
Mar
11
comment Nonconstructible Algebraic Numbers
@IanColey: you mean, that's not constructible in the straightedge and compass sense.
Feb
25
comment Problem regarding limit of the rational function
What is your attempt so far?
Feb
23
comment Is there a function such that $f' = f\circ f$?
Well, if $f'(t) = f(f(t))$, and $f: \mathbb{R} \to (0, \infty)$, then $f'(t) > 0$, so $f$ is increasing everywhere.
Feb
12
comment Global generation of $\mathcal{O}_{\mathbb{P}(\mathcal{E})}(1)$ and $\mathcal{E}$
Ah, right. That was much too fast.
Feb
12
comment Global generation of $\mathcal{O}_{\mathbb{P}(\mathcal{E})}(1)$ and $\mathcal{E}$
I think that locally, the surjection $\mathcal{O}_{\mathbb{P}(\mathcal{E})}^n \to \mathcal{O}_{\mathbb{P}(\mathcal{E})}$ is just Euler sequence, and we know what is the kernel of the Euler sequence - the sheaf of 1-forms. Is this correct? Will this work (I don't recall whether $H^1$ of 1-forms on $\mathbb{P}^{r-1}$ will be zero).
Feb
10
awarded  Promoter
Feb
7
revised Global generation of $\mathcal{O}_{\mathbb{P}(\mathcal{E})}(1)$ and $\mathcal{E}$
added 35 characters in body
Feb
7
asked Global generation of $\mathcal{O}_{\mathbb{P}(\mathcal{E})}(1)$ and $\mathcal{E}$
Feb
7
comment Showing that the Gamma Function (in $\mathbb{R}^+$) is continuous using DCT.
What is $\Gamma(x, y_0)$? The function $\Gamma$ as defined above takes only single argument $y$.
Feb
6
comment Is it enough to check closed immersion at closed points?
Why $f$ factors through $V(I)$?
Feb
6
comment Is it enough to check closed immersion at closed points?
Stalk of $f_* \mathcal{O}_X$ at $f(x)$ is limit of $(f_* \mathcal{O}_X)(U)$ over all neighbourhoods of $f(x)$. But $(f_* \mathcal{O}_X)(U)$ by definition is $\mathcal{O}(f^{-1}(U))$. Now, stalk of $\mathcal{O}_X$ at $x$ again is limit of $\mathcal{O}_X(V)$ over all neighbourhoods $V$ of $x$. Now, since $f$ is closed embedding, every neighbourhood of $x$ is of the form $f^{-1}(U)$ for some $U$.
Feb
5
answered Is it enough to check closed immersion at closed points?