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 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 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.

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.

AMPLE VECTOR BUNDLES WITH SECTIONS VANISHING ON PROJECTIVE SPACES OR QUADRICS

1995 ◽  
Vol 06 (04) ◽  
pp. 587-600 ◽  
Author(s):  
ANTONIO LANTERI ◽  
HIDETOSHI MAEDA
Keyword(s):  
Vector Bundle ◽  
Projective Space ◽  
Complex Manifold ◽  
Vector Bundles ◽  
Projective Spaces ◽  
Compact Complex Manifold ◽  
Ample Vector Bundle ◽  
Zero Locus

Let ɛ be an ample vector bundle of rank r≥2 on a compact complex manifold X of dimension n≥r+1 having a section whose zero locus is a submanifold Z of the expected dimension n–r. Pairs (X, ɛ) as above are classified under the assumption that Z is either a projective space or a quadric.

Complex submanifolds, connections and asymptotics

2010 ◽  
Vol 53 (2) ◽  
pp. 373-383
Author(s):  
Tatyana Foth
Keyword(s):  
Line Bundle ◽  
Complex Manifold ◽  
Compact Complex Manifold ◽  
Line Bundles ◽  
Natural Connection ◽  
Complex Submanifolds ◽  
Positive Line Bundle ◽  
Positive Line

AbstractLet L → X be a positive line bundle on a compact complex manifold X. For compact submanifolds Y, S of X and a holomorphic submersion Y → S with compact fibre, we study curvature of a natural connection on certain line bundles on S.

scholarly journals A characterization of finite vector bundles on Gauduchon astheno-Kahler manifolds

2018 ◽  
Vol Volume 2 ◽  
Author(s):  
Indranil Biswas ◽  
Vamsi Pritham Pingali
Keyword(s):  
Vector Bundle ◽  
Complex Manifold ◽  
Vector Bundles ◽  
Projective Variety ◽  
Polynomial Equation ◽  
Compact Complex Manifold ◽  
Kahler Manifolds ◽  
Galois Covering ◽  
Finite Vector

A vector bundle E on a projective variety X is called finite if it satisfies a nontrivial polynomial equation with integral coefficients. A theorem of Nori implies that E is finite if and only if the pullback of E to some finite etale Galois covering of X is trivial. We prove the same statement when X is a compact complex manifold admitting a Gauduchon astheno-Kahler metric.

scholarly journals ON THE EINSTEIN–KÄHLER METRIC AND THE HOLONOMY OF A LINE BUNDLE

2002 ◽  
Vol 45 (1) ◽  
pp. 83-90
Author(s):  
Kenji Tsuboi
Keyword(s):  
Line Bundle ◽  
Complex Manifold ◽  
Lie Group ◽  
Maximal Compact Subgroup ◽  
Compact Subgroup ◽  
Base Space ◽  
Subject Classification ◽  
Compact Complex Manifold ◽  
Identity Component ◽  
Determinant Line Bundle

AbstractIn this paper we give a relation between the Futaki invariant for a compact complex manifold $M$ and the holonomy of a determinant line bundle over a loop in the base space of any principal $G$-bundle, where $G$ is the identity component of the maximal compact subgroup of the complex Lie group consisting of all biholomorphic automorphisms of $M$. Using the property of the Futaki invariant, we show that the holonomy is an obstruction to the existence of the Einstein–Kähler metrics on $M$. Our main result is Theorem 2.1.AMS 2000 Mathematics subject classification: Primary 32Q20. Secondary 58J28; 58J52

scholarly journals Stable vector bundles on algebraic surfaces II

1973 ◽  
Vol 52 ◽  
pp. 173-195 ◽  
Author(s):  
Fumio Takemoto
Keyword(s):  
Vector Bundle ◽  
Line Bundle ◽  
Vector Bundles ◽  
Ample Line Bundle ◽  
Algebraic Surfaces ◽  
Complex Numbers ◽  
Stable Vector Bundle ◽  
Projective Varieties ◽  
Stable Vector Bundles ◽  
Direct Sum

This paper is a continuation of “Stable vector bundles on algebraic surfaces” [10]. For simplicity we deal with non-singular projective varieties over the field of complex numbers. Let W be a variety whose fundamental group is solvable, let H be an ample line bundle on W, and let f: V → W be an unramified covering. Then we show in section 1 that if E is an f*H-stable vector bundle on V then f*E is a direct sum of H-stable vector bundles. In particular f*L is a direct sum of simple vector bundles if L is a line bundle on V.

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