hyperplane section造句

例句与造句

1. The topology of hyperplane sections is studied in the topic of the Lefschetz hyperplane theorem and its refinements.
2. Because the dimension drops by one in taking hyperplane sections, the process is potentially an inductive method for understanding varieties of higher dimension.
3. The relationship with projective space is that the D for a very ample L corresponds to the hyperplane sections ( intersection with some hyperplane ) of the embedded M.
4. In general such theorems state that homology or cohomology is supported on a hyperplane section of an algebraic variety, except for some'loss'that can be controlled.
5. When " k " is infinite, this open subset then has infinitely many rational points and there are infinitely many smooth hyperplane sections in " X ".
6. It's difficult to find hyperplane section in a sentence. 用hyperplane section造句挺难的
7. The first point comes up if we assume that " V " is given as a projective variety, and the divisors on " V " are hyperplane sections.
8. It can fail for non-K鋒ler manifolds : for example, Hopf surfaces have vanishing second cohomology groups, so there is no analogue of the second cohomology class of a hyperplane section.
9. The second point is that the fibers may themselves'degenerate'and acquire singular points ( where Bertini's lemma applies, the " general " hyperplane section will be smooth ).
10. Over an arbitrary field " k ", there is a dense open subset of the dual space ( \ mathbf P ^ n ) ^ { \ star } whose rational points define hyperplanes smooth hyperplane sections of " X ".
11. He proved theorems on the topology of hyperplane sections of algebraic varieties, which provide a basic inductive tool ( these are now seen as allied to Morse theory, though a Lefschetz pencil of hyperplane sections is a more subtle system than a Morse function because hyperplanes intersect each other ).
12. He proved theorems on the topology of hyperplane sections of algebraic varieties, which provide a basic inductive tool ( these are now seen as allied to Morse theory, though a Lefschetz pencil of hyperplane sections is a more subtle system than a Morse function because hyperplanes intersect each other ).
13. In a more formal statement, specify that " V " is a non-singular projective surface, and let " H " be the divisor class on " V " of a hyperplane section of " V " in a given projective embedding.
14. In algebraic geometry, assuming therefore that " X " is " V ", a subvariety not lying completely in any " H ", the hyperplane sections are algebraic sets with irreducible components all of dimension dim ( " V " ) & minus; 1.
15. For example, the set of points in "'R "'4 such that is a cone, whose " x " 4  constant hyperplane sections give spheres . ( Note that gives a sphere or radius zero . ) You can, of course, construct much more exotic examples .  talk ) 01 : 59, 30 August 2011 ( UTC)
16. For a Fano surface S, a 1-form w defines also a hyperplane section { w = 0 } into "'P "'4 of the cubic F . The zeros of the generic w on S corresponds bijectively to the numbers of lines into the smooth cubic surface intersection of { w = 0 } and F, therefore we recover that the second Chern class of S equals 27.