a = 6, b = 2 are the values

Let **a****xyz – ****a****y^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.

Curvature_surfaces _definition.docx

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7. Describe the symmetries of your surface **V. Is it ** bounded or unbounded?

8. Can you find a line on your surface?