WebAs a functor, it sends any S-scheme T to the group of global sections f of T such that f n = 1. Over an affine base such as Spec A, it is the spectrum of A[x]/(x n −1). If n is not invertible in the base, then this scheme is not smooth. In particular, over a … Web19 de ago. de 2024 · The aim of this article is to prove that, under certain conditions, an affine flat normal scheme that is of finite type over a local Dedekind scheme in mixed characteristic admits infinitely many normal effective Cartier divisors. For the proof of this result, we prove the Bertini theorem for normal schemes of some type. We apply the …
algebraic geometry - Global sections of the projective space ...
Web8 Global sections of line bundles and linear systems. 9 Q-divisors. 10 The Grothendieck–Lefschetz hyperplane theorem. 11 Notes. 12 References. ... In general, however, a Weil divisor on a normal scheme need not be locally principal; see the examples of quadric cones above. Web13 de dez. de 2024 · In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 0358.Beware of the difference between the letter ' O ' and the digit ' 0 '. Tag: Post comment how is whitney thore\u0027s mother
Proj construction - Wikipedia
WebA general remark is that , where denote the section . Definition 28.26.1. reference Let be a scheme. Let be an invertible -module. We say is ample if. is quasi-compact, and. for every there exists an and such that and is affine. Lemma 28.26.2. reference Let be a scheme. Let be an invertible -module. Let . Webwhere x 0 is, as usual, viewed as a global section of the twisting sheaf O(1). (In fact, the above isomorphism is part of the usual correspondence between Weil divisors and Cartier divisors.) Finally, the dual of the twisting sheaf corresponds to the tautological line bundle (see below). Tautological line bundle in algebraic geometry In algebraic geometry, an algebraic variety or scheme X is normal if it is normal at every point, meaning that the local ring at the point is an integrally closed domain. An affine variety X (understood to be irreducible) is normal if and only if the ring O(X) of regular functions on X is an integrally closed domain. A variety X over a field is normal if and only if every finite birational morphism from any variety Y to X is an isomorphism. how is whiting indiana for senior citizens