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?
Needs help with similar assignment?
We are available 24x7 to deliver the best services and assignment ready within 3-4 hours? Order a custom-written, plagiarism-free paper
Math homework helpDo not let math assignments discourage you from trying your best. One of our math experts can help you with math homework online. Our math tutors can help you with any level of algebra, calculus, or geometry. Ask your question to get the support you need 24/7.
Order Over WhatsApp Place an Order Online