scholarly journals Convexité holomorphe intermédiaire des revetements d'un domaine pseudoconvexe

1997 ◽  
Vol 56 (2) ◽  
pp. 285-290
Author(s):  
S. Asserda
Keyword(s):  
Line Bundle ◽  
Complex Manifold ◽  
Pseudoconvex Domain ◽  
Holomorphic Line Bundle ◽  
Hermitian Metric ◽  
Holomorphic Sections ◽  
Positive Holomorphic Line Bundle ◽  
Holomorphic Covering

Let M be a complex manifold and L → M be a positive holomorphic line bundle over M equipped with a Hermitian metric h of class C2. If D ⊂⊂ M is a pseudoconvex domain which is relatively compact in M then there exists an integer r0 such that for every r ≥ r0 and for every connected holomorphic covering π: the covering is holomorphically convex with respect to holomorphic sections of .

scholarly journals Stable Higgs bundles over positive principal elliptic fibrations

2018 ◽  
Vol 5 (1) ◽  
pp. 195-201
Author(s):  
Indranil Biswas ◽  
Mahan Mj ◽  
Misha Verbitsky
Keyword(s):  
Vector Bundle ◽  
Line Bundle ◽  
Complex Manifold ◽  
Higgs Bundle ◽  
Compact Complex Manifold ◽  
Holomorphic Line Bundle ◽  
Higgs Bundles ◽  
Stable Vector Bundle ◽  
Hermitian Metric ◽  
The Third

AbstractLet M be a compact complex manifold of dimension at least three and Π : M → X a positive principal elliptic fibration, where X is a compact Kähler orbifold. Fix a preferred Hermitian metric on M. In [14], the third author proved that every stable vector bundle on M is of the form L⊕ Π ⃰ B0, where B0 is a stable vector bundle on X, and L is a holomorphic line bundle on M. Here we prove that every stable Higgs bundle on M is of the form (L ⊕ Π ⃰B0, Π ⃰ ɸX), where (B0, ɸX) is a stable Higgs bundle on X and L is a holomorphic line bundle on M.

EXAMPLES OF A NON-VANISHING CONJECTURE OF KAWAMATA

2007 ◽  
Vol 18 (05) ◽  
pp. 527-533
Author(s):  
YU-LIN CHANG
Keyword(s):  
Line Bundle ◽  
Complex Manifold ◽  
Symmetric Spaces ◽  
Sufficient Conditions ◽  
Compact Complex Manifold ◽  
Holomorphic Line Bundle ◽  
Compact Type ◽  
Hermitian Symmetric Spaces ◽  
Canonical Line Bundle ◽  
Positive Holomorphic Line Bundle

Let M be a compact complex manifold with a positive holomorphic line bundle L, and K be its canonical line bundle. We give some sufficient conditions for the non-vanishing of H0(M, K + L). We also show that the criterion can be applied to interesting classes of examples including all compact locally hermitian symmetric spaces of non-compact type, Mostow–Siu [10] surfaces, Kähler threefolds given by Deraux [3] and examples of Zheng [17].

scholarly journals Vanishing Theorems on Compact Hyper-kähler Manifolds

Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Qilin Yang
Keyword(s):  
Line Bundle ◽  
Nonnegative Integer ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Holomorphic Line Bundle ◽  
Vanishing Theorems ◽  
Vanishing Theorem ◽  
Positive Holomorphic Line Bundle ◽  
Special Case

We prove that if B is a k-positive holomorphic line bundle on a compact hyper-kähler manifold M, then HpM,Ωq⊗B=0 for P>n+[k/2] with q a nonnegative integer. In a special case, k=0 and q=0, we recover a vanishing theorem of Verbitsky’s with a little stronger assumption.

scholarly journals HIGHER CODIMENSIONAL UEDA THEORY FOR A COMPACT SUBMANIFOLD WITH UNITARY FLAT NORMAL BUNDLE

2018 ◽  
Vol 238 ◽  
pp. 104-136
Author(s):  
TAKAYUKI KOIKE
Keyword(s):  
Line Bundle ◽  
Complex Manifold ◽  
Normal Bundle ◽  
Holomorphic Foliation ◽  
Compact Complex Manifold ◽  
Sufficient Condition ◽  
Existence Problem ◽  
Hermitian Metric ◽  
Flat Normal Bundle ◽  
Compact Submanifold

Let $Y$ be a compact complex manifold embedded in a complex manifold with unitary flat normal bundle. Our interest is in a sort of the linearizability problem of a neighborhood of $Y$. As a higher codimensional generalization of Ueda’s result, we give a sufficient condition for the existence of a nonsingular holomorphic foliation on a neighborhood of $Y$ which includes $Y$ as a leaf with unitary-linear holonomy. We apply this result to the existence problem of a smooth Hermitian metric with semipositive curvature on a nef line bundle.

scholarly journals A note on Berezin-Toeplitz quantization of the Laplace operator

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Alberto Della Vedova
Keyword(s):  
Line Bundle ◽  
Laplace Operator ◽  
Adjoint Operator ◽  
Holomorphic Sections ◽  
The Laplace Operator ◽  
Hodge Manifold

AbstractGiven a Hodge manifold, it is introduced a self-adjoint operator on the space of endomorphisms of the global holomorphic sections of the polarization line bundle. Such operator is shown to approximate the Laplace operator on functions when composed with Berezin-Toeplitz quantization map and its adjoint, up to an error which tends to zero when taking higher powers of the polarization line bundle.

On the Asymptotic Behavior of Complete Kähler Metrics of Positive Ricci Curvature

2010 ◽  
Vol 62 (1) ◽  
pp. 3-18
Author(s):  
Boudjemâa Anchouche
Keyword(s):  
Asymptotic Behavior ◽  
Line Bundle ◽  
Ricci Curvature ◽  
Projective Variety ◽  
Volume Form ◽  
Positive Ricci Curvature ◽  
Standard Type ◽  
Number Of Components ◽  
Holomorphic Sections ◽  
Volume Forms

AbstractLet (X, g) be a complete noncompact Kähler manifold, of dimension n ≥ 2, with positive Ricci curvature and of standard type (see the definition below). N. Mok proved that X can be compactified, i.e., X is biholomorphic to a quasi-projective variety. The aim of this paper is to prove that the L2 holomorphic sections of the line bundle K−qXand the volume form of the metric g have no essential singularities near the divisor at infinity. As a consequence we obtain a comparison between the volume forms of the Kähler metric g and of the Fubini-Study metric induced on X. In the case of dimC X = 2, we establish a relation between the number of components of the divisor D and the dimension of the.

scholarly journals RANK ONE CONNECTIONS ON ABELIAN VARIETIES, II

2012 ◽  
Vol 23 (12) ◽  
pp. 1250125
Author(s):  
INDRANIL BISWAS ◽  
JACQUES HURTUBISE ◽  
A. K. RAINA
Keyword(s):  
Line Bundle ◽  
Exact Sequence ◽  
Abelian Varieties ◽  
Explicit Construction ◽  
The Other ◽  
Holomorphic Line Bundle ◽  
Canonical Isomorphism ◽  
Complex Torus ◽  
Rank One

Given a holomorphic line bundle L on a compact complex torus A, there are two naturally associated holomorphic ΩA-torsors over A: one is constructed from the Atiyah exact sequence for L, and the other is constructed using the line bundle [Formula: see text], where α is the addition map on A × A, and p1 is the projection of A × A to the first factor. In [I. Biswas, J. Hurtvbise and A. K. Raina, Rank one connections on abelian varieties, Internat. J. Math.22 (2011) 1529–1543], it was shown that these two torsors are isomorphic. The aim here is to produce a canonical isomorphism between them through an explicit construction.

scholarly journals A partial converse to the Andreotti–Grauert theorem

2018 ◽  
Vol 155 (1) ◽  
pp. 89-99 ◽  
Author(s):  
Xiaokui Yang
Keyword(s):  
Line Bundle ◽  
Ricci Curvature ◽  
Positive Eigenvalue ◽  
Projective Manifold ◽  
Hermitian Metric ◽  
Partial Converse

Let $X$ be a smooth projective manifold with $\dim _{\mathbb{C}}X=n$. We show that if a line bundle $L$ is $(n-1)$-ample, then it is $(n-1)$-positive. This is a partial converse to the Andreotti–Grauert theorem. As an application, we show that a projective manifold $X$ is uniruled if and only if there exists a Hermitian metric $\unicode[STIX]{x1D714}$ on $X$ such that its Ricci curvature $\text{Ric}(\unicode[STIX]{x1D714})$ has at least one positive eigenvalue everywhere.

Chern-Yamabe problem and Chern-Yamabe soliton

2021 ◽  
Vol 32 (03) ◽  
pp. 2150016
Author(s):  
Pak Tung Ho ◽  
Jinwoo Shin
Keyword(s):  
Scalar Curvature ◽  
Complex Manifold ◽  
The Other ◽  
Compact Complex Manifold ◽  
Yamabe Problem ◽  
Conformal Metric ◽  
Hermitian Metric ◽  
Dimension Formula ◽  
Complex Dimension ◽  
Yamabe Soliton

Let [Formula: see text] be a compact complex manifold of complex dimension [Formula: see text] endowed with a Hermitian metric [Formula: see text]. The Chern-Yamabe problem is to find a conformal metric of [Formula: see text] such that its Chern scalar curvature is constant. In this paper, we prove that the solution to the Chern-Yamabe problem is unique under some conditions. On the other hand, we obtain some results related to the Chern-Yamabe soliton.

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