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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 Actions 7. Describe the symmetries of your surface V. Is it bounded or unbounded? 8. Can you find a line on your surface? .
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a = 6, b = 2 are the valuesLet axyz - ay^3+xz^2 =.docx
- 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 Actions 7. Describe the symmetries of your surface V. Is it bounded or unbounded? 8. Can you find a line on your surface?
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