# Marra

Brazil

 2d comment How to prove that any regular map $\phi : \Bbb P^1 \to \Bbb A^n(\Bbb C)$ maps $\Bbb P^1$ to point.When you wrote $\phi$ as quotients of functions in each coordinate that's exactly the coordinates you need. To understand this geometrically check out the charts in the Riemann Sphere (which is biholomorphic to $\mathbb{P}^1$ and therefore both are compact). By "globally holomorphic" I meant that it descends to an entire funtion (holomorphic in the entire complex plane).] 2d answered How to prove that any regular map $\phi : \Bbb P^1 \to \Bbb A^n(\Bbb C)$ maps $\Bbb P^1$ to point. Jan 21 comment Virtual Euler Characteristic of a Curve in Brunella's paperI am certainly more proficient in subjects not deeply related to the ones related to this question. Nice quotation! Jan 20 comment Virtual Euler Characteristic of a Curve in Brunella's paperNice to have you around, one more for me to pester with my newbie questions! Jan 20 comment Virtual Euler Characteristic of a Curve in Brunella's paperYou're almost two years late! By the way the question was an exercise from your advisor :P Dec 14 accepted Isomorphism between $Hom(E,F)$ and $E^*\otimes F$, E and F vector bundles. Dec 12 awarded Popular Question Nov 23 asked Isomorphism between $Hom(E,F)$ and $E^*\otimes F$, E and F vector bundles. Nov 9 awarded Student Nov 9 asked Is this Orc and Hobgoblin hybrid well balanced? Oct 15 awarded Scholar Oct 15 accepted How is foliation of manifolds' theory useful in General Relativity? Oct 12 comment Can I have a linear map from $\mathbb{R}^n$ to $\mathbb{R}^m$?Oh, not at all. For example, think on $f(x)=x^3$, which is not linear as a function form $\mathbb{R}$ to itself and $f(0)=0$. Oct 12 comment Can I have a linear map from $\mathbb{R}^n$ to $\mathbb{R}^m$?For linearity, it must obey the rules $T(x+y)=T(x)+T(y)$ and, for an scalar $\alpha$, $T(\alpha x) = \alpha T(x)$. Note that these rules imply that T(0)=0. To show this, try using $T(x)=T(x+0)$. Sep 27 comment Is there a function $f : \mathbb Z \times \mathbb Z \to \mathbb Z$ that is one to one and onto?I was thinking about a real, continuous function since it was tagged as a Real Analysis question. Totally missed the countability of them. Sep 27 comment Is there a function $f : \mathbb Z \times \mathbb Z \to \mathbb Z$ that is one to one and onto?How do you know it exists? Sep 26 comment Real Analysis Open sets & Open BallsTake, for example, the subset $\{ (x,y)\in\mathbb{R}^2 : |x|<1,|y|<1\}$. It's the interior of the square of side size 2, centered at the origin of $\mathbb{R}^2$. It's possible to prove that this set is open and it is obviously not a ball. Sep 26 comment Real Analysis Open sets & Open BallsA counter example on what? An open set that is not a ball? Sep 26 comment Evaluating an integral in mathematicaWhat, specifically, is, "crap out"? Sep 26 comment entension of a holomorphic map on projective algebraic manifoldsI would like to see this question answered too. Don't know which paper it came from, though.