共查询到20条相似文献,搜索用时 15 毫秒
1.
Chin-Yu Hsiao 《偏微分方程通讯》2017,42(6):895-942
Let M be an arbitrary complex manifold and let L be a Hermitian holomorphic line bundle over M. We introduce the Berezin–Toeplitz quantization of the open set of M where the curvature on L is nondegenerate. In particular, we quantize any manifold admitting a positive line bundle. The quantum spaces are the spectral spaces corresponding to [0,k?N], where N>1 is fixed, of the Kodaira Laplace operator acting on forms with values in tensor powers Lk. We establish the asymptotic expansion of associated Toeplitz operators and their composition in the semiclassical limit k→∞ and we define the corresponding star-product. If the Kodaira Laplace operator has a certain spectral gap this method yields quantization by means of harmonic forms. As applications, we obtain the Berezin–Toeplitz quantization for semi-positive and big line bundles. 相似文献
2.
Bernard Shiffman 《中国科学A辑(英文版)》2008,51(4):707-720
We show that the zeros of random sequences of Gaussian systems of polynomials of in- creasing degree almost surely converge to the expected limit distribution under very general hypotheses. In particular,the normalized distribution of zeros of systems of m polynomials of degree N,orthonor- malized on a regular compact set K(?)C~m,almost surely converge to the equilibrium measure on K as N→∞. 相似文献
3.
Arnaud Beauville 《manuscripta mathematica》2003,110(3):343-349
Let C be a curve of genus g and L a line bundle of degree 2g on C. Let ML be the kernel of the evaluation map . We show that when L is general enough, the rank g bundle ML and its exterior powers are stable, but admit a reducible theta divisor.
Received: 16 September 2002 / Revised version: 29 October 2002 Published online: 14 February 2003
Mathematics Subject Classification (2000): 14H60 相似文献
4.
Elena Rubei 《manuscripta mathematica》2002,108(1):135-137
We exhibit an example of a line bundle M on a smooth complex projective variety Y s.t. M satisfies Property N
10
, the 10-module of a minimal resolution of the ideal of the embedding of Y by M is nonzero and M
2
does not satisfy Property N
10
. Thus this is a completely convincing example showing that surprisingly it is not true that if a line bundle M satisfies Property N
p
then any power of M satisfies Property N
p
. We recall that in [Ru] we proved the following statement: if M is a line bundle on a smooth complex projective variety and M satisfies Property N
p
then M
s
satisfies Property N
p
if s≥p.
Received: 5 March 2001 相似文献
5.
Ling Yang 《Calculus of Variations and Partial Differential Equations》2009,35(4):409-420
For an arbitrary Dirac-harmonic map (φ,ψ) between compact oriented Riemannian surfaces, we shall study the zeros of |ψ|. With the aid of Bochner-type formulas, we explore the relationship between the order of the zeros of |ψ| and the genus of M and N. On the basis, we could clarify all of non-trivial Dirac-harmonic maps from S
2 to S
2. 相似文献
6.
We show that ifM is the total space of a holomorphic bundle with base space a simply connected homogeneous projective variety and fibre and
structure group a compact complex torus, then the identity component of the automorphism group ofM acts trivially on the Dolbeault cohomology ofM. We consider a class of compact complex homogeneous spacesW, which we call generalized Hopf manifolds, which are diffeomorphic to S1 ×K/L whereK is a compact connected simple Lie group andL is the semisimple part of the centralizer of a one dimensional torus inK. We compute the Dolbeault cohomology ofW. We compute the Picard group of any generalized Hopf manifold and show that every line bundle over a generalized Hopf manifold
arises from a representation of its fundamental group. 相似文献
7.
Summary If (M, ω) is a compact symplectic manifold andL ⊂M a compact Lagrangian submanifold and if φ is a Hamiltonian diffeomorphism ofM then the V. Arnold conjecture states (possibly under additional conditions) that the number of intersection section points
ofL and φ (L) can be estimated by #{Lϒφ (L)}≥ cuplength +1. We shall prove this conjecture for the special case (L, M)=(ℝP
n
, ℂP
n
) with the standard symplectic structure. 相似文献
8.
XiaoJiang Tan 《中国科学A辑(英文版)》2008,51(4):721-727
In this paper,we give some conditions on the surjective of multiply maps H~0(R,L)×H~0(R,K)→H~0(R,L(?)K).Here R is a compact Riemann surface,L a line bundle on R and K is the canonical line bundle. 相似文献
9.
We study the natural almost CR structure on the total space of a subbundle of hyperquadrics of the tangent bundle T(M) over a semi-Riemannian manifold (M, g) and show that if the Reeb vector ξ of an almost contact Riemannian manifold is a CR map then the natural almost CR structure on M is strictly pseudoconvex and a posteriori ξ is pseudohermitian. If in addition ξ is geodesic then it is a harmonic vector field. As an other application, we study pseudoharmonic vector fields on a compact strictly pseudoconvex CR manifold M, i.e. unit (with respect to the Webster metric associated with a fixed contact form on M) vector fields X ε H(M) whose horizontal lift X↑ to the canonical circle bundle S1 → C(M) → M is a critical point of the Dirichlet energy functional associated to the Fefferman metric (a Lorentz metric on C(M)). We show that the Euler–Lagrange equations satisfied by X↑ project on a nonlinear system of subelliptic PDEs on M.
Mathematics Subject Classifications (2000): 53C50, 53C25, 32V20 相似文献
10.
11.
Elena Rubei 《manuscripta mathematica》2000,101(4):449-455
Let M be a very ample line bundle on a smooth complex projective variety Y and let ϕ
M
:Y→P(H
0(Y, M)*) be the map associated to M; we are concerned with the problem to see whether the syzygies of ϕ
M
(Y) give information on the syzygies of ϕ
M
s
(Y). In particular we prove that if Y is a smooth complex projective variety and M is a line bundle on Y satisfying Property
N
p
, then M
s
satisfies Property N
p
if s≥p.
Received: 11 June 1999 / Revised version: 22 November 1999 相似文献
12.
We study the geometric behavior of the normal bundle T
⊥
M of a submanifold M of a Riemannian manifold . We compute explicitely the second fundamental form of T
⊥
M and look at the relation between the minimality of T
⊥
M and M. Finally we show that the Maslov forms with respect to a suitable connection of the pair (T
⊥
M, are null.
Received March 14, 2001; in revised form February 11, 2002 相似文献
13.
V. V. Shurygin 《Journal of Mathematical Sciences》2011,177(5):758-771
The Lie jet L
θ
λ of a field of geometric objects λ on a smooth manifold M with respect to a field θ of Weil A-velocities is a generalization of the Lie derivative L
v
λ of a field λ with respect to a vector field v. In this paper, Lie jets L
θ
λ are applied to the study of A-smooth diffeomorphisms on a Weil bundle T
A
M of a smooth manifold M, which are symmetries of prolongations of geometric objects from M to T
A
M. It is shown that vanishing of a Lie jet L
θ
λ is a necessary and sufficient condition for the prolongation λ
A
of a field of geometric objects λ to be invariant with respect to the transformation of the Weil bundle T
A
M induced by the field θ. The case of symmetries of prolongations of fields of geometric objects to the second-order tangent bundle T
2
M are considered in more detail. 相似文献
14.
Alan Weinstein 《Journal of the European Mathematical Society》2000,2(1):53-86
We define a C
1 distance between submanifolds of a riemannian manifold M and show that, if a compact submanifold N is not moved too much under the isometric action of a compact group G, there is a G-invariant submanifold C
1-close to N. The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure
combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds
as zeros of sections of extended normal bundles.
Received September 14, 1999 / final version received November 29, 1999 相似文献
15.
Let B be a fiber bundle with compact fiber F over a compact Riemannian n-manifold M
n. There is a natural Riemannian metric on the total space B consistent with the metric on M. With respect to that metric, the volume of a rectifiable section σ: M → B is the mass of the image σ(M) as a rectifiable n-current in B.
Theorem 1. For any homology class of sections of B, there is a mass-minimizing rectifiable current T representing that homology class which is the graph of a C1 section on an open dense subset of M.
Mathematics Subject Classifications (2000): 49F20, 49F22, 49F10, 58A25, 53C42, 53C65. 相似文献
16.
Izu Vaisman 《Monatshefte für Mathematik》1990,109(4):305-310
IfM is a Riemannian manifold, andL is a Lagrangian submanifold ofT
*
M, the Maslov class ofL has a canonical representative 1-form which we call theMaslov form ofL. We prove that ifL =v
*
N = conormal bundle of a submanifoldN ofM, its Maslov form vanishes iffN is a minimal submanifold. Particularly, ifM is locally flatv
*
N is a minimal Lagrangian submanifold ofT
*
M iffN is a minimal submanifold ofM. This strengthens a result of Harvey and Lawson [H L]. 相似文献
17.
The maximal Seshadri number μ(L) of an ample line bundle L on a smooth projective variety X measures the local positivity of the line bundle L at a general point of X. By refining the method of Ein-Küchle-Lazarsfeld, lower bounds on μ(L) are obtained in terms of L
n
, n=dim(X), for a class of varieties. The main idea is to show that if a certain lower bound is violated, there exists a non-trivial
foliation on the variety whose leaves are covered by special curves. In a number of examples, one can show that such foliations
must be trivial and obtain lower bounds for μ(L). The examples include the hyperplane line bundle on a smooth surface in ℙ3 and ample line bundles on smooth threefolds of Picard number 1.
Received: 29 June 2001 / Published online: 16 October 2002
RID="⋆"
ID="⋆" Supported by Grant No. 98-0701-01-5-L from the KOSEF.
RID="⋆⋆"
ID="⋆⋆" Supported by Grant No. KRF-2001-041-D00025 from the KRF. 相似文献
18.
David G. Ebin 《Geometric And Functional Analysis》2012,22(1):202-212
Let M be a compact manifold with a symplectic form ω and consider the group Dw{\mathcal{D}_\omega} consisting of diffeomorphisms that preserve ω. We introduce a Riemannian metric on M which is compatible with ω and use it to define an L
2-inner product on vector fields on M. Extending by right invariance we get a weak Riemannian metric on Dw{\mathcal{D}_\omega} . We show that this metric has geodesics which come from integral curves of a smooth vector field on the tangent bundle of
Dw{\mathcal{D}_\omega} . Then, estimating the growth of such geodesics, we show that they extend globally. 相似文献
19.
We study the weighted integral transform on a compact manifold with boundary over a smooth family of curves Γ. We prove generic
injectivity and a stability estimate under the condition that the conormal bundle of Γ covers T
*
M.
Second author was partly supported by NSF Grant DMS-0400869; third author was partly supported by NSF and a Walker Family
Endowed Professorship. 相似文献
20.
Erwann Delay 《manuscripta mathematica》2007,123(2):147-165
Let (M =]0, ∞[×N, g) be an asymptotically hyperbolic manifold of dimension n + 1 ≥ 3, equipped with a warped product metric. We show that there exist no TT L
2-eigentensors with eigenvalue in the essential spectrum of the Lichnerowicz Laplacian Δ
L
. If (M, g) is the real hyperbolic space, there is no symmetric L
2-eigentensors of Δ
L
. 相似文献