1. Why did you mention wanting to become a police if you are not interested in criminal law? It seemed odd to read at first but have to tie into….
a = 6, b = 2 are the values
Let axyz – ay^3 +xz^2 =bw^3 be a homogenous polynomial in P3(x,y,z,w), describing an algebraic variety V in P3.
1. Show the view of V in affine patches Ux, Uy, Uz, Uw. when x=1,y=1, z=1, w=1.
2. What is the dimension of V?
3. Is V an irreducible variety?
4. Find all singular points.
5. Give the ideal of V. Is it prime? Is your variety irreducible? Describe the ring k(V) = O(V) of polynomials (regular functions) on V.
6. Calculate curvature at (at least two) smooth points.
7. Describe the symmetries of your surface V. Is it bounded or unbounded?
8. Can you find a line on your surface?