a = 6, b = 2 are the valuesLetaxyz –ay^3 +xz^2=bw^3be a homogenous polynomial inP3(x,y,z,w), describing an algebraic variety V inP3.1. Show the view of V in affine patchesUx, 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 ofV.Is it prime? Is your variety irreducible? Describe the ring k(V) = O(V) of polynomials (regular functions) onV.6. Calculate curvature at (at least two) smooth points.Curvature_surfaces _definition.docxActions7. Describe the symmetries of your surfaceV. Is itbounded or unbounded?8. Can you find a line on your surface?