WebMar 6, 2024 · An effective Cartier divisor on X is an ideal sheaf I which is invertible and such that for every point x ... { X \times_S S', }[/math] and this pullback is an effective Cartier … WebEnter the email address you signed up with and we'll email you a reset link.

1 Cartier and Weil divisors - Columbia University

WebWhen we later address a characteristic-free notion of non-degeneracy for quadratic spaces that works uniformly even over any ring (including $\ZZ/4\ZZ$ and $\ZZ$ in which 2 may be a nonzero nilpotent or a non-unit that is not a zero-divisor), the smoothness of the projective quadric $(q=0)$ will be the right perspective for defining non-degeneracy. Let X be an integral Noetherian scheme. Then X has a sheaf of rational functions All regular functions are rational functions, which leads to a short exact sequence A Cartier divisor on X is a global section of An equivalent description is that a Cartier divisor is a collection where is an open cover of is a section of on and on up to multiplication by a section of Cartier divisors also have a sheaf-theoretic description. A fractional ideal sheaf is a sub--module … the lion guard rafiki

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WebnonCartierLocus-- the non-Cartier locus of a Weil divisor; negativePart, see positivePart-- get the effective part or anti-effective part of a divisor; positivePart-- get the effective part or … WebAn R-divisor is called ample if it can be written as a positive linear combination of ample Cartier divisors.) It follows from Kleiman's criterion that, for X projective, every nef R … WebPullbacks in precategories; 2.36. Sieves in categories; 2.37. ... The greatest common divisor of integers; 4.47. The greatest common divisor of natural numbers; 4.48. ... Cartier's … the lion guard return of the pridelands