affine variety in a sentence
1) We shall show it is locally an affine variety .
affine collocations
2) Thus it is an affine algebraic variety .
3) An irreducible affine algebraic set is also called an affine variety .
affine variety example sentences
4) Notice that every affine variety is quasi-projective.5) The affine varieties is a subcategory of the category of the algebraic sets.
6) Just as Spec replaces affine varieties , the Proj construction replaces projective varieties in modern algebraic geometry.
7) An affine variety is a "rational variety" if it is birationally equivalent to an affine space.
8) Here we show "X" admits a structure of variety by showing locally it is an affine variety .
9) Affine varieties can be given a natural topology by declaring the closed sets to be precisely the affine algebraic sets.
10) Affine group varieties are known as linear algebraic groups, since they can be embedded as subgroups of general linear groups.
11) More generally, there is an antitone Galois connection between ideals in the ring and subschemes of the corresponding affine variety .
12) Using regular functions from an affine variety to A1, we can define regular maps from one affine variety to another.
13) Using regular functions from an affine variety to A1, we can define regular maps from one affine variety to another.
14) The general linear group "GL""n" is an affine algebraic variety that can be viewed as the multiplicative group of the "n" by "n" matrix ring variety.
15) If "X" is an affine algebraic variety , then the set of all regular functions on "X" forms a ring called the coordinate ring of "X".
example sentences with affine variety
16) It allows you to glue affine varieties (along common open sets) without worrying whether the resulting object can be put into some projective space.17) An " affine variety " over an algebraically closed field is conceptually the easiest type of variety to define, which will be done in this section.
18) This establishes that the above equation, clearly a generalization of the previous one, defines the Zariski topology on any affine variety .
19) Two affine varieties are "birationally equivalent" if there two rational functions between them which are inverse one to the other in the regions where both are defined.
20) "X'" is an affine variety .
21) By definition, an affine rational variety of dimension "k" may be described by parametric equations of the form
22) (Many authors use the phrase " affine variety " to refer to any affine algebraic set, irreducible or not)
23) are affine varieties .
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