Globally generated sheaf

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August undefined, 2024

WebLet X be a projective scheme with ample, globally generated sheaf OX(1) and coherent sheaf F. Then λ(F) ≤ tif and only if F is (t,t)-regular. We can now merge, and thus slightly strengthen, [S, Lemma 1.4] and [A1, Lemma 3.7]. The reader may also confer [Ca, Section 3] for similar proofs for WebAug 17, 2024 · Let X be a scheme, M a quasi-coherent sheaf, then M is globally generated if it is generated by global sections, i.e. if there exist sections s i ∈ M ( X), i ∈ I with I a …

Section 17.4 (01AL): Sections of sheaves of modules—The Stacks …

WebApr 18, 2024 · A visionary and forward-thinking transformation leader, I am passionate about building, architecting, and operationalizing strategies, … 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 … homes orlando vacation

Chern class of direct image sheaf - MathOverflow

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 … 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 … Web(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 hirsch leather strap amazon

Stability of Syzygy Sheaves Associated to Rank One Torsion …

Ample invertible sheaves - University of California, San Diego

WebStack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, … WebDe nition. Given a Riemann surface C, we call the abelian di erential a global (1;0)-form on C, i.e. a di erential one-form that locally can be written as f(z)dz, with fa holomorphic function. We call geometric genus, denoted by p g, the dimen-sion of the C-vector space given by the abelian di erentials. homes orleans maWebRemark 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). homes otto circle fayetteville ga

"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

Chern class of direct image sheaf - MathOverflow

Web33.35 Coherent sheaves on projective space. 33.35. Coherent sheaves on projective space. In this section we prove some results on the cohomology of coherent sheaves on over a field which can be found in [ Mum]. These will be useful … 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 ...

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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 … Weband let ff c(Rm be a globally generated sheaf omodules. Then ff is globally coherent. MODULES OVER SHEAVES OF HOLOMORPHIC FUNCTIONS 49 Thedefinition of global coherencehasbuiltintoit ananalogueof Cartan’s ... andif ff is the kernel of,then ff is globally generated. Let be givenbythemap (al, a) ...

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., … WebMay 15, 2010 · Suppose that for any invertible sheaf H, there exists α 0 such that the Frobenius amplitude φ (G α ⊗ H)lessorequalslanttfor αgreaterorequalslantα 0 .Then {G α } isat-amplefilter. 6. F-amplitude of an ample vector bundle Let E be an ample vector bundle. If chark = 0, then φ (E)

WebA 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 … 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 …

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WebSince generates , its image generates , implying . Therefore . Because is affine, it is separated by Schemes, Lemma 26.21.15, and we conclude . Lemma 28.26.8. Let be a … home sound prewiring theaterWebApr 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. homes orlando areaWebLbe 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 home sound deadeningWebTheorem. (M-regularity criterion) Let F be a coherent sheaf and L an invertible sheaf supported on a subvariety Y of the abelian variety X (possibly X itself). If both F and L … hirsch leather watch bandsWebAug 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. hirschleifer analysisWebsay 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. … hirsch leather watch strapWebIn 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. hirsch leather straps