Tagged Questions

Surface is a two-dimensional submanifold of three-dimensional Euclidean space.

32 views

53 views

Vector parametrization of a surface intersection

How does one parametrize the following curve in 3-space to $\vec{g}(t): [a, b] \to \mathbb{R}^3$: the intersection of $x^2+y^2+z^2=a^2$ and $x+y+z=0$ ? What I could come up with is as follows: ...
52 views

Solving a 2nd-order elliptic PDE with non-constant coefficients

I wonder how I can solve the following 2nd-order PDE on the positive semiplane $\{x>0\}$: $$(\partial_x^2+\frac{1}{x}\partial_y^2)\phi=\delta(x-x_0)\delta(y).$$ I notice that the l.h.s. is the ...
80 views

What line bundle pulls back to the trivial line bundle

Let $X$ be an abelian surface. $C$ be a curve in $X$. Consider the projective bundle $\pi:\mathbb{P}^1_C\longrightarrow C$. This is a projective morphism. I have two questions : 1) Can we find an ...
27 views

Volume and surface of knock out drum

I have to calculate the volume and the surface of some KO drums (knock out drum). To avoid ambiguous understandings here's a picture of one: http://www.zamilsteel.com/ped/images/projects/11.jpg I ...
What is the type of the surfaces $x^5 - y^5 + z^2 + x=0$ and $x^5 - y^5 + z^2 + x+1=0$?
I am interested what is the type of the surfaces over the rationals $$x^5 - y^5 + z^2 + x=0$$ and $$x^5 - y^5 + z^2 + x+1=0$$ Magma's ...
Let $X$ be an abelian surface over $\mathbb{C}$. And let $i:X\longrightarrow X$ be the inverse map. $i$ is a degree 2 morphism. We consider $Y$ the quotient of $X$ by the action of $i$, that is, ...