0
votes
1answer
25 views

Find all the intersection points of a vector parabola (in R3) and a sphere

Given that I have a vector in R3 (7t, 10t - 2t^2, 5t) | (These numbers are arbitrary for the sake of the process) A sphere centered at the point ( 15, 25, 10) with a radius of 20 There is a ...
2
votes
0answers
141 views

intersection multiplicity and tangents

I haven't been able to find a proof of the following fact, which I have seen mentioned a few times: two non-singular curves have multiplicity intersection greater than 1 at a point P if and only if ...
0
votes
1answer
115 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
122 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
99 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
818 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 ...