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Globally generated sheaf

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WebOct 31, 2014 · In this paper, Gotzmann's Regularity Theorem is established for globally generated coherent sheaves on projective space. This is used to extend Gotzmann's explicit construction to the Quot scheme. The Gotzmann representation is applied to bound the second Chern class of a rank 2 globally generated coherent sheaf in terms of the … WebAug 1, 2024 · A line bundle is globally generated if and only if it is basepoint-free. For example, every quasi-coherent sheaf on an affine scheme is globally generated. [6] Analogously, in complex geometry, Cartan's theorem A says that every coherent sheaf on a Stein manifold is globally generated.

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Web30.9 Coherent sheaves on locally Noetherian schemes. 30.9. Coherent sheaves on locally Noetherian schemes. We have defined the notion of a coherent module on any ringed space in Modules, Section 17.12. Although it is possible to consider coherent sheaves on non-Noetherian schemes we will always assume the base scheme is locally … Web1.4. We then classify characters such that the general sheaf is globally generated in §5. We close the paper with some remarks on the open question of determining the Chern characters of ample vector bundles. Acknowledgements. We would like to thank Aaron Bertram, Lawrence Ein, John Lesieutre, and Daniel Levine for useful discussions. 2 ... chemist warehouse thyroid support

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WebApr 1, 2024 · Take a hyperelliptic curve X of genus g ≥ 3 and let P be a 2-torsion line bundle on X, such that P = OC(p − q), where p, q are distinct Weierstrass points. Now set L = ωC ⊗ P. Since L has strictly positive degree on a curve, it is ample. Moreover, by Serre duality, h1(C, L) = h0(C, P) = 0, hence h0(C, L) = g − 1 > 2 by Riemann-Roch. WebA sheaf of grain on a plaque. Sheafing machine. A sheaf (/ʃiːf/) is a bunch of cereal-crop stems bound together after reaping, traditionally by sickle, later by scythe or, after its introduction in 1872, by a mechanical reaper … Websay that Fis globally generated if there are elements s i 2( X;F), i 2I such that for every point x 2X, the images of s i in the stalk F x, generate the stalk as an O X;x-module. Lemma 10.21. Let X be a scheme and TFAE (1) Fis globally generated. (2) The natural map H0(X;F) O X! F ; is surjective. (3) Fis a quotient of a free sheaf. Proof. Clear. chemist warehouse tinea cream

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Web''Suppose F is a finite type quasicoherent sheaf on a scheme X. Show that F is globally generated at p if and only if “the fiber of F is generated by global sections at p ”, i.e., … WebRemark 1.6. Being globally generated is not an open condition. However, it is an open condition among sheaves with vanishing higher cohomology. Let Ebe a sheaf with vanishing higher coho-mology. If a⁄0, then h0pX;Eq⁄rand E˛Or X, hence Ecannot be globally generated. It is easy to classify Ewith a 1 which are globally generated (see Remark8.14). chemist warehouse timingsWebStack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, … chemist warehouse tingalpa

"WebApr 17, 2024 · 3. Let X be a smooth, projective curve (over C) of genus at least 2 and E be a globally generated sheaf on X. I am looking for conditions/examples such that there … " - Globally generated sheaf

Globally generated sheaf

WebLbe an ample and globally generated line bundle. Suppose (A;e 2’) be a pseudo-e ective line bundle and I(’) is the multiplier ideal sheaf. If the numerical dimension of (A;’) is not zero, i.e. nd(A;’) 6= 0 , then (1.1) K X L n A I(’) is globally generated. A key ingredient in the proof of Theorem 1.3 relies on vanishing theorems WebSep 2016 - Present6 years 8 months. United States. Caribbean-American Cultural Arts Foundation is a national organization, based in Atlanta, Georgia. We are a non-profit …

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Web0, the sheaf F⌦Ln is generated by its global sections. This is equivalent to say that: Lm is very ample for some m>0. Example 90. (1) Every invertible sheaf on an ane variety (or a scheme) X is ample, since every coherent sheaf on X is generated by its global sections. (2) Let X = Pn k be the projectiven-space. The sheaf O X(d) is ample if ... WebApr 18, 2024 · A visionary and forward-thinking transformation leader, I am passionate about building, architecting, and operationalizing strategies, …

WebApr 10, 2024 · As the USCO and other agencies begin to screen for AI-generated content in material, Magnani said the market for tools that analyze AI is also set to grow in areas … WebIf F is a nite type sheaf, show that F is generated by global sections at p if and only if ﬁthe ber of F is generated by global sections at pﬂ, i.e. the map from global sections to the …

WebDefinition 17.8.1. Let be a ringed space. Let be a sheaf of -modules. We say that is locally generated by sections if for every there exists an open neighbourhood of such that is globally generated as a sheaf of -modules. In other words there exists a set and for each a section such that the associated map. is surjective. WebApr 17, 2024 · Let X be a smooth, projective curve (over C) of genus at least 2 and E be a globally generated sheaf on X. I am looking for conditions/examples such that there exists a closed point x ∈ X for which the natural morphism from H0(End(E)) to End(E)x is surjective, where End(E)x denotes the fiber of the vector bundle.

WebOct 31, 2014 · In this paper, Gotzmann's Regularity Theorem is established for globally generated coherent sheaves on projective space. This is used to extend Gotzmann's …

Web1. O(m) of P n R is globally generated if and only if m>=0. If F(m) is globally generated then F(n) is globally generated for n>m. 2. Suppose M and N are R-modules and F, G are associated sheaves on Spec R. Show that the tensor product of F and G is associated with a tensor product of M and N (Hint: tensor product of modules commutes with ... flight ottawa to laWebSep 18, 2024 · They proved that M-regular sheaves are indeed continuously globally generated. Debarre gave a nice characterization: a coherent sheaf \(\mathscr {F}\) is continuously globally generated if and only if there exists \(M\in {\mathbb Z}\) such that \(\mu _M^*\mathscr {F}\otimes Q\) is globally generated for any \(Q\in … chemist warehouse times openWebLet be a sheaf of -modules. We say that is generated by global sections if there exist a set , and global sections , such that the map which is the map associated to on the … flight oslo to tromsohttp://www.personal.psu.edu/jwh6013/Research/globallygeneratedvb.pdf flight oslo new yorkWebIn particular, if Eis generated by global sections, i.e. if there is a surjection: On S →Efor some n then π: P(E) ⊂Pn−1 S →Sis a projective morphism. Definition.An invertible sheaf Lon Sis ample if for each coherent sheaf F, there is a n F∈Z such that F⊗L⊗n are generated by global sections for all n≥n F. chemist warehouse tingalpa jobsWeb(2) A line bundle L on X is very ample if and only if L ⊗ Ix is globally generated for all x ∈ X. Thus the very ampleness problem can be reduced to global generation. (3) If X ⊂ Pn, then the global generation of the twisted ideal sheaf IX(d) implies that X is locally cut out by equations of degree d. Similarly, if X is a subvariety of a flight ottawa to addis ababa chemist warehouse tingalpa email