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projective completion造句

例句與造句

  1. The process outlined above, used to obtain it, is called " projective completion " or " projectivization ".
  2. 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.
  3. 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 ).
  4. This is a nonsingular algebraic curve of genus one defined over \ mathbb { Q }, and its projective completion is an elliptic curve over \ mathbb { Q }.
  5. 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.
  6. It's difficult to find projective completion in a sentence. 用projective completion造句挺難的
  7. 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 ).
  8. 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 ).
  9. 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.
  10. 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.
  11. 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 ).
  12. 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.
  13. 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.

相鄰詞匯

  1. "projective bundle"造句
  2. "projective capacitive"造句
  3. "projective class group"造句
  4. "projective closure"造句
  5. "projective collineation"造句
  6. "projective configuration"造句
  7. "projective conic"造句
  8. "projective connection"造句
  9. "projective coordinate"造句
  10. "projective coordinates"造句
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