0
votes
1answer
59 views

Build equation of a curve with set of coordinates

I need to calculate the intersection of two curves. I do not have the equation of the curves, but I will have a finite set of coordinates. Is there a way to build the equation for this curve based ...
2
votes
0answers
102 views

Intersection of a cone $x^2+y^2-z^2$ and a generic plane in $\mathbb{RP}^3$

If we take the zero locus of $x^2+y^2-z^2$ to be our cone, I'd like to know how to go about finding the intersection of the cone and a generic plane $Ax+By+Cz+Dw=0$. The result will be a conic, but ...
2
votes
1answer
73 views

Is the intersection of the diagonal with a graph always transverse in characteristic zero

Let X be a projective smooth connected curve over $\mathbf{C}$. Let $f:X\to X$ be a non-constant morphism. Is the intersection of the diagonal $\Delta_X$ and the graph $\Gamma_f$ on $X\times X$ ...
0
votes
3answers
654 views

Intersection of Cubic curves

This is the question which i am attempting to solve, and it seems to difficult to get rid of the exponents. Show that a the two cubic curves $Y^3 = X^2 + X^3$ and $X^3 = Y^2 + Y^3$ intersect in ...