Pull back of cartier divisor

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August undefined, 2024

WebC with a Cartier divisor. The clumsy way to do this is to proceed as above, and deform the divisor to a linearly equivalent divisor, which does not contain the curve. A more sophisticatedapproach is as follows. If the image of the curve lies in the divisor, then instead of pulling the divisor back, pullback the associated line bundle and take ... WebJun 2, 2016 · In general one cannot pull back Weil divisors. But you are in an extremely special case where (a) you are pulling back by an automorphism, and (b) your variety is …

CARTIER DIVISORS - University of Chicago

WebOn the level of divisors, we have a Weil divisor D on X ⇒ D U is a Cartier divisor on U. For a Cartier divisor E on U, its Zariski closure D is a Weil divisor on X. We already see what … WebCwith a Cartier divisor. The clumsy way to do this is to proceed as above, and deform the divisor to a linearly equivalent divisor, which does not contain the curve. A more sophisticated approach is as follows. If the image of the curve lies in the divisor, then instead of pulling the divisor back, pullback the associated line bundle and take ... does a private practice need a type 2 npi

Pullback of a Divisor - Mathematics Stack Exchange

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 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 … WebThe group of Cartier divisors on Xis denoted Div(X). 2.5. Some notation. To more closely echo the notation for Weil divisors, we will often denote a Cartier divisor by a single … does a probiotic help with constipation

arXiv:math/0211335v1 [math.AG] 21 Nov 2002

WebLet 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. 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. eye on keyser facebookWebPullback of a Divisor. Let f: X → Y be a finite, separable morphism of curves (curve: integral scheme, of dimension 1, proper over an algebraically closed field with all local rings … does a private pension affect social security

"WebRelative effective Cartier divisors. The following lemma shows that an effective Cartier divisor which is flat over the base is really a “family of effective Cartier divisors” over the … " - Pull back of cartier divisor

Pull back of cartier divisor

Do there exist linear relations between exceptional divisors

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. WebApr 6, 2024 · If there is a nontrivial linear relation among the Cartier divisor classes $[E_i]$ in $\widetilde{X}$, then this pulls back to a nontrivial linear relation among the pullback Cartier divisor classes on $\widehat{Y}$. By the argument above, the irreducible components of the exceptional locus on $\widehat{Y}$ are $\mathbb{Z}$-linearly independent.

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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 ). Web(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.

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 … 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

WebA 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. … http://math.stanford.edu/~vakil/245/245class6.pdf

WebSep 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 …

Web1.4. For a rational 1-contraction α: X99K Y, we may deﬁne the pull-back of any R-Cartier divisor Das follows: α∗D def= g ∗h ∗D(it is easy to show that this deﬁnition does not depend on the choice of the hut (1.2)). Note however that the map α∗ is not functorial: it is possible that (α β)∗ does not coincide with β∗α∗. does a probiotic help with digestive issuesWebGiven 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 ... does a probiotic help with ibsWebDec 1, 2015 · Suppose that f: X → Z is a surjective morphism of normal varieties with connected fibers. Then an R -Cartier divisor L on X is f -numerically trivial if and only if there is an R -Weil divisor D on Z such that D is numerically Q -Cartier and f ⊛ D ≡ L where f ⊛ is the numerical pullback of [14]. The proof runs as follows. does a probiotic help with diverticulitisWebIn this case the linear system can be recovered by pulling back the hyperplane sections of Y ˆPm 1 and in fact O X(D) = ˚O Pn(1). 1. De nition 3.2. ... Let Dbe a Q-Cartier divisor on Y. (1) If Dis ample and fis nite then f Dis ample. (2) If f is surjective and f Dis ample (this can only happen if f is nite) then Dis ample. does a processor help fpsWebLemma : Let f: Y → X be a proper morphism of varieties such that that. R f ∗ O X = O Y. Let E be a Cartier divisor on Y. Then E is the pull back of a Cartier divisor on X if and only if for all x ∈ X, there is a neighborhood U of x in X such that E restricted to f − 1 ( U) is trivial. Let x ∈ X, and let U be a contractible ... eye on international education associationWeband 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 ... does a probiotic help with acid refluxWeban open source textbook and reference work on algebraic geometry does a probiotic help with gas and bloating