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 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.

Projective manifolds of sectional genus three as zero loci of sections of ample vector bundles

2008 ◽  
Vol 144 (1) ◽  
pp. 109-118 ◽  
Author(s):  
ANTONIO LANTERI ◽  
HIDETOSHI MAEDA
Keyword(s):  
Vector Bundles ◽  
Projective Variety ◽  
Ample Line Bundle ◽  
Global Section ◽  
Sectional Genus ◽  
Ample Vector Bundle ◽  
Complex Projective Variety ◽  
Projective Manifolds ◽  
Complex Projective ◽  
Zero Locus

AbstractLet ϵ be an ample vector bundle of rank r ≥ 2 on a smooth complex projective variety X of dimension n such that there exists a global section of ϵ whose zero locus Z is a smooth subvariety of dimension n-r ≥ 2 of X. Let H be an ample line bundle on X such that the restriction HZ of H to Z is very ample. Triplets (X, ϵ, H) with g(Z, HZ) = 3 are classified, where g(Z, HZ) is the sectional genus of (Z, HZ).

scholarly journals Continuous CM-regularity of semihomogeneous vector bundles

2020 ◽  
Vol 20 (3) ◽  
pp. 401-412
Author(s):  
Alex Küronya ◽  
Yusuf Mustopa
Keyword(s):  
Vector Bundle ◽  
Abelian Variety ◽  
Upper Bound ◽  
Vector Bundles ◽  
Projective Variety ◽  
Constant Function ◽  
Piecewise Constant Function ◽  
Piecewise Constant ◽  
Generic Vanishing

AbstractWe ask when the CM (Castelnuovo–Mumford) regularity of a vector bundle on a projective variety X is numerical, and address the case when X is an abelian variety. We show that the continuous CM-regularity of a semihomogeneous vector bundle on an abelian variety X is a piecewise-constant function of Chern data, and we also use generic vanishing theory to obtain a sharp upper bound for the continuous CM-regularity of any vector bundle on X. From these results we conclude that the continuous CM-regularity of many semihomogeneous bundles — including many Verlinde bundles when X is a Jacobian — is both numerical and extremal.

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 A remark on stability and restrictions of vector bundles to hypersurfaces

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Ernesto C. Mistretta
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Projective Variety ◽  
Smooth Projective Variety

AbstractWe prove that a vector bundle on a smooth projective variety is (semi)stable if the restriction on a fixed ample smooth subvariety is (semi)stable.

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.

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 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.

Special varieties in adjunction theory and ample vector bundles

2001 ◽  
Vol 130 (1) ◽  
pp. 61-75 ◽  
Author(s):  
A. LANTERI ◽  
H. MAEDA
Keyword(s):  
Vector Bundles ◽  
Projective Variety ◽  
Global Section ◽  
Smooth Projective Variety ◽  
Ample Vector Bundle ◽  
Projective Varieties ◽  
Adjunction Theory ◽  
Set Up ◽  
Important Position ◽  
Smooth Projective Varieties

In this paper varieties are always assumed to be defined over the field [Copf ] of complex numbers.Given a smooth projective variety Z, the classification of smooth projective varieties X containing Z as an ample divisor occupies an extremely important position in the theory of polarized varieties and it is well-known that the structure of Z imposes severe restrictions on that of X. Inspired by this philosophy, we set up the following condition ([midast ]) in [LM1] in order to generalize several results on ample divisors to ample vector bundles:([midast ]) [Escr ] is an ample vector bundle of rank r [ges ] 2 on a smooth projective variety X of dimension n such that there exists a global section s ∈ Γ([Escr ]) whose zero locus Z = (s)0 is a smooth subvariety of X of dimension n − r [ges ] 1.

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.

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