complete intersection造句

例句与造句

1. Finally, it is possible to generalize the above construction and formula to complete intersection morphisms; this extension is discussed in ?6.6 . as well as Ch . 17 of loc . cit.
2. Fano surfaces are perhaps the simplest and most studied examples of irregular surfaces of general type that are not related to a product of two curves and are not a complete intersection of divisors in an Abelian variety.
3. For example, taking quadrics in " P " 3 again, ( 2, 2 ) is the multidegree of the complete intersection of two of them, which when they are in general position is an elliptic curve.
4. In geometric terms, it follows that a local complete intersection subscheme " Y " of any scheme " X " has a normal bundle which is a vector bundle, even though " Y " may be singular.
5. If " V " is a hypersurface there need only be one equation, and for complete intersections the number of equations can be taken as the codimension; but the general projective variety has no defining set of equations that is so transparent.
6. It's difficult to find complete intersection in a sentence. 用complete intersection造句挺难的
7. In the case of surfaces in a space of dimension three, every surface is a complete intersection, and a surface is defined by a single polynomial, which is irreducible or not, depending if non-irreducible algebraic sets of dimension two are considered as surfaces or not.
8. complete intersection local ring which is factorial in codimension at most 3 ( for example, if the non-regular locus of " R " has codimension at least 4 ), then " R " is a unique factorization domain ( and hence every Weil divisor on Spec ( " R " ) is Cartier ).
9. If, on the side of caution, we assume complete intersection, and, on the other hand, no intersection at all among all other ancestries, we would get a minimum of 83.11 % " Portuguese ", " Portuguese-Brazilian ", and " Brazilian " ancestries, vs 39.97 % of " All Others ".
10. A classic example is the twisted cubic in \ mathbb { P } ^ 3 : it is a set-theoretic complete intersection, i . e . as a set it can be expressed as the intersection of 2 hypersurfaces, but not an ideal-theoretic ( or scheme-theoretic ) complete intersection, i . e . its homogeneous ideal cannot be generated by 2 elements.
11. A classic example is the twisted cubic in \ mathbb { P } ^ 3 : it is a set-theoretic complete intersection, i . e . as a set it can be expressed as the intersection of 2 hypersurfaces, but not an ideal-theoretic ( or scheme-theoretic ) complete intersection, i . e . its homogeneous ideal cannot be generated by 2 elements.
12. Geometrically, we have the following : if " X " is a local complete intersection in a nonsingular variety; e . g ., " X " itself is nonsingular, then " X " is Cohen-Macaulay; i . e ., the stalks \ mathcal { O } _ p of the structure sheaf are Cohen-Macaulay for all prime ideals p.
13. Globally, every codimension-1 subvariety of projective space is defined by the vanishing of one homogeneous polynomial; by contrast, a codimension-" r " subvariety need not be definable by only " r " equations when " r " is greater than 1 . ( That is, not every subvariety of projective space is a complete intersection . ) Locally, every codimension-1 subvariety of a smooth variety can be defined by one equation in a neighborhood of each point.
14. If " R " has dimension greater than 0 and " x " is an element in the maximal ideal that is not a zero divisor then " R " is a complete intersection ring if and only if " R " / ( " x " ) is . ( If the maximal ideal consists entirely of zero divisors then " R " is not a complete intersection ring . ) If " R " has dimension 0, then showed that it is a complete intersection ring if and only if the Fitting ideal of its maximal ideal is non-zero.
15. If " R " has dimension greater than 0 and " x " is an element in the maximal ideal that is not a zero divisor then " R " is a complete intersection ring if and only if " R " / ( " x " ) is . ( If the maximal ideal consists entirely of zero divisors then " R " is not a complete intersection ring . ) If " R " has dimension 0, then showed that it is a complete intersection ring if and only if the Fitting ideal of its maximal ideal is non-zero.
16. If " R " has dimension greater than 0 and " x " is an element in the maximal ideal that is not a zero divisor then " R " is a complete intersection ring if and only if " R " / ( " x " ) is . ( If the maximal ideal consists entirely of zero divisors then " R " is not a complete intersection ring . ) If " R " has dimension 0, then showed that it is a complete intersection ring if and only if the Fitting ideal of its maximal ideal is non-zero.
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