Pull back of cartier divisor
WebTheorem 1.1 (Pull-back of quasi-log structures). ... Notation 2.1. A pair [X,ω] consists of a scheme X and an R-Cartier divisor (or R-line bundle) ω on X. In this paper, a scheme means a separated scheme of finite type over SpecC. A variety is a …
Pull back of cartier divisor
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WebGiven a pseudo-divisor Don a variety Xof dimension X, we can de ne the Weil class divisor [D] by taking D~ to be the Cartier divisor which represents Dand setting [D] := [D~], the associated Weil divisor from the previous section. The above lemma shows that this yields a well-de ned element of A n 1X; this gives a homomorphism from the group of ... WebJan 10, 2024 · and well done. $\blacksquare$ Section 1.3. The Cone of Curves of Smooth Varieties. Definition 1.15. More properties of extremal faces and rays we refer chapter 18 (especially Theorem 18.5) in book [Convex97] 1 which is important for us to read the Mori’s theory. $\blacksquare$ Theorem 1.24.
WebAs of last day, you know: Pseudo-divisors pull back. And if X is a variety, any pseudo-divisor on X is represented by some Cartier divisor on X. (A Cartier divisor D represents apseudo-divisor (L,Z,s)if D ⊂ Z, andthere isanisomorphism OX(D) → Lwhich away form Z takes sD (the “canonical section”) to s.) Furthermore, if Z 6= X, D is uniquely WebDefinition 31.26.2. Let X be a locally Noetherian integral scheme. A prime divisor is an integral closed subscheme Z \subset X of codimension 1. A Weil divisor is a formal sum D = \sum n_ Z Z where the sum is over prime divisors of X and the collection \ { Z \mid n_ Z \not= 0\} is locally finite (Topology, Definition 5.28.4 ).
WebOnly the line bundle, the support, and the trivialization are needed to carry out the above intersection construction’. These concepts are formalized in the notation of a pseudo-divisor (§ 2.2); there is the added advantage that a pseudo-divisor, unlike the stricter notion of a Cartier divisor, pulls back under arbitrary morphisms WebAug 29, 2011 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site
WebAug 24, 2013 · Definition 1. A rational map f is said to be almost holomorphic fibration if there exists a Zariski open set U such that the induced map f _ {U}:U \rightarrow S is a proper morphism with connected fibres. We recall the definition of the pull back of a Cartier divisor by a rational map.
WebTo go back from line bundles to divisors, the first Chern class is the isomorphism from the Picard group of line bundles on a variety X to the group of Cartier divisors modulo linear equivalence. Explicitly, the first Chern class c 1 ( L ) {\displaystyle c_{1}(L)} is the divisor ( s ) of any nonzero rational section s of L . office 365 email storage archiveWebof ideals on Z (i.e. the pullback of O/I is an effective Cartier divisor), then there exists a unique morphism g : Z → X˜ factoring f. Z _ g_ _// f >˚˚ >>> >>> > X˜ π X In other words, if you have a morphism to X, which, when you pull back the ideal I, you get an effective Cartier divisor, then this factors through X˜ → X. my chart bendWeband let Dbe a relative Cartier divisor for the projection map S×X→S. There exists a reduced scheme T and a relative Cartier divisor D˜ for the projection map T×X→T, ... We apply Noetherian induction on Z. By pulling back along Zred ֒→Z, we may assume that Zis reduced. Let η֒→Zbe a generic point of an irreducible component. To ... office 365 email webhookWebLet B Z X denote the blow-up of X along Z and E Z ⊂ B Z X the exceptional divisor. We refer to π: B Z X → X as a blow-up if we imagine that B Z X is created from X, and a blow-down if we start with B Z X and construct X later. Note that E Z has codimension 1 and Z has codimension ≥ 2. Thus a blow-down decreases the Picard number by 1. office 365 email tools and ms office downloadWebA relative effective Cartier divisor is an effective Cartier divisor D ˆX such that the projection D !X is flat. We will show that this notion is well behaved under base-change by any S0!S. Lemma 1. Suppose D ˆX is a relative effective Cartier divisor for f : X !S. For any S0!S, denote by f0: X0!S0the pullback. Then D0= S0 S D ˆX0is a ... mychart bend or bmcWebSep 26, 2024 · Already is an effective Cartier divisor on , and the pullback of is the strict transform plus the exceptional divisor . One way to see this is to deform to a hyperplane … office 365 e mail verteiler anlegenWeb(b) Recall the definition of D ·[V]: We pull the pseudo-Cartier divisor D back to V. We take any Cartier divisor giving that pseudo-divisor (let me sloppily call this D as well). We then take the Weil divisor corresponding to that Cartier divisor: D 7→ P W ordW(D). This latter is a group homomorphism. mychart bend memorial clinic