affine cone in a sentence

1. This is the affine cone over the projective quadric " S ".
2. The cone may have multiple branches, each one an affine cone over a simple closed curve in the projective tangent space.
3. The dual curve is a curve in the projective tangent space at the point, and the affine cone over this curve is the Monge cone.
4. Geometrically, this definition means that the degree of " X " is the multiplicity of the vertex of the affine cone over " X ".
5. :If no seven points out of are co-conic, then the vector space of cubic homogeneous polynomials that vanish on ( the affine cones of ) ( with multiplicity for double points ) has dimension two.
6. It's difficult to find affine cone in a sentence.
7. :If no seven points out of lie on a non-degenerate conic, and no four points out of lie on a line, then the vector space of cubic homogeneous polynomials that vanish on ( the affine cones of ) has dimension two.
8. Since will always contain the whole line through on account of B閦out's theorem, the vector space of cubic homogeneous polynomials that vanish on ( the affine cones of ) is isomorphic to the vector space of quadratic homogeneous polynomials that vanish ( the affine cones of ), which has dimension two.
9. Since will always contain the whole line through on account of B閦out's theorem, the vector space of cubic homogeneous polynomials that vanish on ( the affine cones of ) is isomorphic to the vector space of quadratic homogeneous polynomials that vanish ( the affine cones of ), which has dimension two.