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?
.
a = 6, b = 2 are the valuesLet axyz - ay^3+xz^2 =.docx
1. 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
.
2. 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?
