scholarly journals A Vanishing Theorem

2005 ◽  
Vol 180 ◽  
pp. 35-43 ◽  
Author(s):  
F. Laytimi ◽  
W. Nahm
Keyword(s):  
Vector Bundle ◽  
Tensor Product ◽  
Vector Bundles ◽  
Vanishing Theorem ◽  
Dolbeault Cohomology ◽  
Ample Vector Bundle ◽  
Exterior Powers ◽  
Parameter Values

AbstractThe main result is a general vanishing theorem for the Dolbeault cohomology of an ample vector bundle obtained as a tensor product of exterior powers of some vector bundles. It is also shown that the conditions for the vanishing given by this theorem are optimal for some parameter values.

Ample Vector Bundles of Curve Genus One

1999 ◽  
Vol 42 (2) ◽  
pp. 209-213 ◽  
Author(s):  
Antonio Lanteri ◽  
Hidetoshi Maeda
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Projective Variety ◽  
Ample Vector Bundle ◽  
Smooth Complex ◽  
Complex Projective Variety ◽  
Curve Genus ◽  
Genus One ◽  
Complex Projective ◽  
Zero Locus

AbstractWe investigate the pairs (X, ε) consisting of a smooth complex projective variety X of dimension n and an ample vector bundle ε of rank n − 1 on X such that ε has a section whose zero locus is a smooth elliptic curve.

On the Classification of Lie Pseudo-Algebras

1970 ◽  
Vol 22 (5) ◽  
pp. 905-915 ◽  
Author(s):  
Ngö van Quê
Keyword(s):  
Vector Bundle ◽  
Exact Sequence ◽  
Tensor Product ◽  
Vector Bundles ◽  
Canonical Morphism ◽  
Image Position

For every ( differentiable) bundle E over a manifold M, Jk(E) denotes the set of all k-jets of local (differentiable) sections of the bundle E. Jk(E) is a bundle over M such that if X is a section of E, thenis a (differentiable) section of Jk(E). If E is a vector bundle, Jk(E) is a vector bundle and we have the canonical exact sequence of vector bundleswhere Sk(T*) is the symmetric Whitney tensor product of the cotangent vector bundle T* of M. and π is the canonical morphism which associates to each k-jet of section its jet of inferior order.

scholarly journals On fuzzy subbundles of vector bundles

2003 ◽  
Vol 2003 (40) ◽  
pp. 2553-2565
Author(s):  
V. Murali ◽  
G. Lubczonok
Keyword(s):  
Vector Bundle ◽  
Tensor Product ◽  
Vector Bundles ◽  
Tangent Bundles

This paper considers fuzzy subbundles of a vector bundle. We define the operations sum, product, tensor product,Hom, and intersection of fuzzy subbundles and in each case, we characterize the corresponding flag of vector subbundles. We then propose two alternative definitions of integrability on fuzzy subbundles of a given type and discuss their naturality, merits, and shortcomings. We do these here with a view to introduce and study integrable fuzzy subbundles of tangent bundles on manifolds and foliations in further papers.

scholarly journals Some Adjunction Properties of Ample Vector Bundles

2001 ◽  
Vol 44 (4) ◽  
pp. 452-458
Author(s):  
Hironobu Ishihara
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Projective Variety ◽  
Sectional Genus ◽  
Genus Zero ◽  
Ample Vector Bundle

AbstractLet ε be an ample vector bundle of rank r on a projective variety X with only log-terminal singularities. We consider the nefness of adjoint divisors KX +(t−r) det ε when t ≥ dim X and t > r. As an application, we classify pairs (X, ε) with cr-sectional genus zero.

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.

scholarly journals P-Ample Bundles and Their Chern Classes

1971 ◽  
Vol 43 ◽  
pp. 91-116 ◽  
Author(s):  
David Gieseker
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Line Bundles ◽  
Chern Classes ◽  
Ground Field ◽  
Ample Vector Bundle

In [9], Hartshorne extended the concept of ampleness from line bundles to vector bundles. At that time, he conjectured that the appropriate Chern classes of an ample vector bundle were positive, and it was hoped that there would be some criterion for ampleness of vector bundles similar to Nakai’s criterion for line bundles. In the same paper, Hartshorne also introduced the notion of p-ample when the ground field had characteristic p, proved that a p-ample bundle was ample and asked if the converse were true.

Restriction properties for the Krull–Schmidt decomposition of vector bundles

2018 ◽  
Vol 29 (03) ◽  
pp. 1850022
Author(s):  
Mihai Halic
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
The Other ◽  
Flag Varieties ◽  
Schmidt Decomposition ◽  
Ample Vector Bundle ◽  
Projective Varieties ◽  
Splitting Criterion ◽  
Irreducible Components ◽  
Smooth Projective Varieties

We obtain decomposability criteria for vector bundles on smooth projective varieties [Formula: see text] by comparing the Krull–Schmidt decomposition on [Formula: see text], on one hand, and along the vanishing locus of a section in an ample vector bundle over [Formula: see text], on the other hand. We determine effective bounds for the amplitude of and also genericity conditions for its sections which ensure that the irreducible components of and those of its restriction correspond bijectively. Moreover, we get a simple splitting criterion for vector bundles on partial flag varieties.

scholarly journals AMPLE VECTOR BUNDLES WITH SECTIONS VANISHING ON SPECIAL VARIETIES

1999 ◽  
Vol 10 (06) ◽  
pp. 677-696 ◽  
Author(s):  
MARCO ANDREATTA ◽  
GIANLUCA OCCHETTA
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Projective Manifold ◽  
Ample Vector Bundle ◽  
Smooth Submanifold ◽  
Del Pezzo ◽  
Complex Projective ◽  
Zero Locus

Let ε be an ample vector bundle of rank r on a complex projective manifold X such that there exists a section s ∈ Γ(ε) whose zero locus Z = (s = 0) is a smooth submanifold of the expected dimension dim X-r:= n - r. Assume that Z is not minimal; we investigate the hypothesis under which the extremal contractions of Z can be lifted to X. Finally we study in detail the cases in which Z is a scroll, a quadric bundle or a del Pezzo fibration.

scholarly journals Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lara B. Anderson ◽  
James Gray ◽  
Magdalena Larfors ◽  
Matthew Magill ◽  
Robin Schneider
Keyword(s):  
Vector Bundles ◽  
Geometric Approach ◽  
Low Energy ◽  
Geometric Features ◽  
Vanishing Theorems ◽  
Vanishing Theorem ◽  
Alternative Derivation ◽  
Yukawa Couplings ◽  
Geometric Methods ◽  
Higher Dimensional

Abstract Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results used differential geometric methods to explain the origin of some of this structure [1, 2]. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.

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