Hermitian line bundle

Author: wehz

August undefined, 2024

http://library.msri.org/books/Book50/files/04Ai.pdf 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 ...

Curvature of a Complex Line Bundle and Hermitian Line Bundle

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 … 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 Hermitian vector bundle of arbitrary rank) on a Riemannian manifold of bounded geometry. We establish an off-diagonal Gaussian upper bound for the associated … intersectionalism and christanity

Finsler Geometry on Complex Vector Bundles

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 … Witryna12 gru 2024 · We know L is a line bundle, so L ( x) is an complex one dimensional vector space. So if we want to find a hermitian metric on L ( x), it is enough to find a … Witrynaline bundle over the parameter space. l will show that the twisting of this line bundle affects the phase of quantum mechanical wave functions. Berry, in a beautiful recent paper, 'discovered a striking phenomenon in the quantum adiabatic theorem. ' That theorem says' that if H(t), 0 ~ t ~1, is a family of Hermitian Hamiltonians, de-pending ... new fantasy fiction 2023

Line Bundles. Honours 1996 - University of Adelaide

Chern–Weil and Hilbert–Samuel Formulae for Singular Hermitian Line Bundles

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… 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 ⊗ … new fantasy authorsWitrynaHermitian 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 intersectionalism meaning

"Witryna27 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. " - Hermitian line bundle

Hermitian line bundle

WitrynaDeterminant line bundles entered diﬀerential geometry in a remarkable paper of Quillen [Q]. He attached a holomorphic line bundle L to a particular family of Cauchy-Riemann operators over a Riemann surface, constructed a Hermitian metric on L, and calculated its curvature. At about the same time Atiyah and WitrynaRICCI CURVATURES ON HERMITIAN MANIFOLDS 3 where his an arbitrary smooth Hermitian metric on L. Note that − √ −1∂∂logh is the (local) curvature form Θ h of the Hermitian line bundle (L,h). If we choose a diﬀerent metric h0, then Θ h0 −Θ h = √ −1∂∂log h h0 is globally ∂∂-exact. Hence cAC

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WitrynaA Hermitian line bundle Lover Xis called ample if the following three conditions are satis ed. (a) The generic bre L Q is ample. (b) The Hermitian line bundle Lis relatively semipositive: the curvature of Lis semipositive and deg(Lj C) > 0 for any closed curve Con any special bre of Xover Spec(Z). Witrynaline bundle on Y0together with a hermitian metric h0of semi-positive curvature, which may be singular. Assume that the curvature current can be extended to Y as a positive, closed current !. Then there ex-ists a holomorphic line bundle (L;h) with a singular hermitian met-ric of semi-positive curvature, whose restriction to Y0is isomorphic to

WitrynaHermitian line bundle pK´1 X,hq. We can view the metric h as a volume form Ωh. Let π : E Ñ X be a holomorphic vector bundle and H be a Hermitian metric on the bundle. In this paper, we consider the following coupled equations:? ´1 ľ ω FH “ λId α0 2 ˜ ş Ωh X Ωh ´ ωn ş X ω n ¸ ´α1 2 pn´2q! trpFH ^FHq ^ωn´2 “ Cvol˜ ω ... Witryna1. 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.

Witrynaof Hermitian-Einstein vector bundles on 2-tori preserving the eigenspaces of a natural Laplace operator. Motivated by the Coherent State Trans-form approach to theta functions [7,22], we extend the latter to vector valued thetas and develop an additional algebraic reinterpretation of Mat-sushima’s theory making FMN-duality manifest again. 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

Witryna17 maj 2014 · 2 Answers. Yes. For ample implies positive, use the fact that c 1 ( O ( 1)) on projective space is the Kähler form of the Fubini-Study metric, and then restrict to …

WitrynaAmple line bundles 85 2.2. Ample vector bundles 88 3. Finsler Connections 91 3.1. Finsler connection 92 3.2. Curvature 94 3.3. Holomorphic sectional curvature 97 4. Ruled Manifolds 99 4.1. Projective bundle 99 ... Hermitian line bundle (L;g) whose Chern form c1(L;g) is positive-de nite, ... new fantasy desechablesWitryna9 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 … intersectional impactWitrynaWe 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 … new fantasy cricket sites 2019