Hermitian line bundle

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Witryna1 sie 1995 · Let X be an arithmetic variety, let L be a hermitian line bundle, and let 1I·lIsup denote the supremum norm on r(XR' LlR) : II/lIsup = sup 11/1I(x). xEX(C) Theorem (1.4). Let X be an arithmetic variety of dimension d, and let Land N be two hermitian line bundle on X such that LQ is ample and L is relatively WitrynaSingular Hermitian holomorphic line bundles X compact, irreducible, normal complex space, dim X = n ˇ: L ! X holomorphic line bundle on X: X = S U , U open, g 2O X (U \U ) are the transition functions. H0(X;L) = space of global holomorphic sections of L, dimH0(X;L) <1 Singular Hermitian metric h on L: f’ 2L1 loc (U ;! n)g such that ...

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WitrynaThis book is the first to give a textbook exposition of Riemann surface theory from the viewpoint of positive Hermitian line bundles and Hörmander $\bar \partial$ estimates. It is more analytical and PDE oriented than prior texts in the field, and is an excellent introduction to the methods used currently in complex geometry, as exemplified ... WitrynaConsidering M being a complex n − dimensional manifold, the tangent bundle T M to M can be seen as a holomorphic vector bundle. In fact, if we consider T M C := T M ⊗ … family medicine the woodlands texas

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WitrynaHermitian holomorphic line bundles whose Chern curvature satisfy a natural growth condition, instead of sequences of powers .Lp;hp/of a ﬁxed line bundle .L;h/. Recall that, by the results of Tian[57](see also Ma and Marinescu[40, Section 5.3]), if .X;!/is a compact Kähler manifold whose Kähler form is integral and Witryna8 CHAPTER 1. HERMITIAN VECTOR BUNDLES ON ARITHMETIC CURVES If E is a Hermitian vector bundle of rank N, one also writes det(E) for AltN E.(1) B.4. Homomorphisms.. — Let E1 ˘(E1,h1) and E2 ˘(E2,h2) be hermitian vector bun- dles (coherent sheaf) over S.The module E ˘ Hom(E1,E2) of oK-linear homomor- phisms … Witrynawith a nef hermitian line bundle L 1 and and an eﬀective hermitian line bundle E, which induces a bijection Hb0(L 1) → Hb0(L). The eﬀectivity of E also gives vol(c L) ≥ vol(c L 1) = L 2 1. Then the result is obtained by applying Theorem B to L 1. See Theorem 3.1. The above implication is inspired by the arithmetic Zariski decom- family medicine thomasville al

$Abstract arXiv:2212.01043v2 [math.DG] 17 Dec 2024$

Are "ample" and "positive" line bundle the same concept?

http://www.cmls.polytechnique.fr/perso/chen/pentmax.pdf WitrynaSingular hermitian metrics on positive line bundles Jean-Pierre Demailly Universit´e de Grenoble I, Institut Fourier, BP 74, Laboratoire associ´e au C.N.R.S. n˚188, F-38402 … cooler box price makroWitryna27 sie 2024 · h(F)≥0.LetN be aholomorphicline bundle onX. We assumethat there exist positive integers a and b and an ample line bundle H on Y such that N ⊗a f∗H b. Thenweobtainthat Hi(Y,Rjf ∗(K X ⊗F⊗J(h)⊗N))=0 for every i>0 and j,whereK X is the canonical bundle of X and J(h) is the multiplieridealsheafofh. Remark 1.6. family medicine thmg/pcp

"Witryna10 sie 2011 · This book is the first to give a textbook exposition of Riemann surface theory from the viewpoint of positive Hermitian line bundles and Hormander $\bar \partial$ estimates. It is more analytical and PDE oriented than prior texts in the field, and is an excellent introduction to the methods used currently in complex geometry, as … " - Hermitian line bundle

Hermitian line bundle

Witryna1. I think, unitary connection refers to a compatible connection on the principal U ( n) -bundle P → M (for some n ). If you associate with P a hermitian vector bundle E → … Witryna7 sty 2015 · 7-Hermitian Line Bundle with Connection: The line bundles used in geometric quantization have two additional structures: 1- A Hermitian metric: on each …

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WitrynaWe consider a family of semiclassically scaled second-order elliptic differential operators on high tensor powers of a Hermitian line bundle (possibly, twisted by an auxiliary … WitrynaA hermitian line bundle L on an arithmetic variety is presented by a couple (L, 11 11), where L is an invertible sheaf on X and 11 11 is a continuous hermitian metric on Lc, which is invariant under the complex conjugation of Xc. If X is an arithmetic surface and 1 is a nonzero meromorphic section of Lc, then we have a linear function

WitrynaWe show that normalized currents of integration along the common zeros of random -tuples of sections of powers of singular Hermitian big line bundles on a compact Kähler manifold distribute asymptotically to the wedge… Witryna24 mar 2024 · A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open set in R^n. Then a positive definite Hermitian matrix H defines a Hermitian metric by =v^(T)Hw^_, where w^_ is the complex conjugate of w. By …

http://staff.ustc.edu.cn/~zhlei18/index_files/positivity-ning.pdf WitrynaProof of Theorem 3: For (Xc, gc) a compact Hermitian symmetric space, the cotangent bundle (T*(Xc), g*) is a Her-mitian vector bundle of seminegative curvature. Let (A, z*) be the corresponding Hermitian line bundle on PT*(X). Then cl(A, g*) is negative semidefinite everywhere. Let At(Xc) be defined similar to At(X) in Theorem 1. In terms of

Witrynafor semi-positive line bundles on compact Ka¨hler manifolds by the theory of harmonic integrals, and Takegoshi in [Tak95] gave a relative version of Enoki’s injectivity for Ka¨hler morphisms. We recently obtained a further generalization of them for pseudo-eﬀective line bundles with singular hermitian metrics by a combination of the theory of

Witrynaa positive line bundle, (E;h) be a (singular) Hermitian vector bundle (maybe of in nite rank) over X, and p >0. (1)(E;h) satis es the optimal L p -estimate condition if for family medicine the buckWitrynaThe curvature of the Chern connection is a (1, 1)-form. For details, see Hermitian metrics on a holomorphic vector bundle. In particular, if the base manifold is Kähler and the … family medicine thomaston gaWitryna9 lip 2024 · Definition. More generally, a line bundle L on a proper scheme X over a field k is said to be nef if it has nonnegative degree on every (closed irreducible) curve in X. ( The degree of a line bundle L on a proper curve C over k is the degree of the divisor (s) of any nonzero rational section s of L.)A line bundle may also be called an invertible … family medicine tigardWitryna1. Extension of line bundles. THEOREM 1. Let S be an analytic subset of at least codimension 2 of the ball B in Cn, and (L, h) be a holomorphic Hermitian line bundle defined on B\S. If the curvature ω of(L, h) is integrable, then L extends to the whole ball B as a holomorphic line bundle. PROOF. cooler box prices in kenyaWitryna25 maj 2005 · Let Lbe a holomorphic, hermitian line bundle over the total space X. Our substitute for the Bergman spaces A2 t is now the space of global sections. CURVATURE OF VECTOR BUNDLES 533 over each ber of L K X t, E t= ( X t;LjX t K X t); where K X t is the canonical bundle of, i.e. the bundle of forms of bidegree (n;0) family medicine thomasville gaWitrynaLet (X, ω) be a weakly pseudoconvex Kähler manifold, Y ⊂ X a closed submanifold defined by some holomorphic section of a vector bundle over X, and L a Hermitian … family medicine tiptonWitryna22 lip 2015 · Abstract. We prove a general extension theorem for holomorphic line bundles on reduced complex spaces, equipped with singular hermitian metrics, whose curvature currents can be extended as ... family medicine temple tx