projective completion造句
例句與造句
- The process outlined above, used to obtain it, is called " projective completion " or " projectivization ".
- Thus, parallel hyperplanes, which did not meet in the affine space, intersect in the projective completion due to the addition of the hyperplane at infinity.
- The problem of resolution of singularities is to know if every algebraic variety is birationally equivalent to a variety whose projective completion is nonsingular ( see also smooth completion ).
- This is a nonsingular algebraic curve of genus one defined over \ mathbb { Q }, and its projective completion is an elliptic curve over \ mathbb { Q }.
- This point of view is commonly expressed by calling " points at infinity " of the affine curve the points ( in finite number ) of the projective completion that do not belong to the affine part.
- It's difficult to find projective completion in a sentence. 用projective completion造句挺難的
- The non-singular plane algebraic curves of degree 2 are called conic sections, and their projective completion are all isomorphic to the projective completion of the circle ( that is the projective curve of equation ).
- The non-singular plane algebraic curves of degree 2 are called conic sections, and their projective completion are all isomorphic to the projective completion of the circle ( that is the projective curve of equation ).
- This allows to consider that an affine curve and its projective completion are the same curve, or, more precisely that the affine curve is a part of the projective curve that is large enough to well define the " complete " curve.
- An affine space is a Zariski-open subset of a projective space, and since any closed affine subset U can be expressed as an intersection of the projective completion \ bar { U } and the affine space embedded in the projective space, this implies that any affine variety is quasiprojective.
- Conversely, one passes from an affine surface to its associated projective surface ( called " projective completion " ) by homogenizing the defining polynomial ( in case of surfaces in a space of dimension three ), or by homogenizing all polynomials of the defining ideal ( for surfaces in a space of higher dimension ).
- For example, if " V " is an affine curve given by, say, y ^ 2 = x ^ 3 + ax + b in the affine plane, then its projective completion in the projective plane is given by y ^ 2 z = x ^ 3 + ax z ^ 2 + b z ^ 3.
- The consideration of the " projective completion " of the two curves, which is their prolongation " at infinity " in the projective plane, allows to quantify this difference : the point at infinity of the parabola is a Riemann-Roch theorem implies that the cubic curve must have a singularity, which must be at infinity, as all its points in the affine space are regular.