Vanishing theorems for tensor powers of an ample vector bundle

1988 ◽  
Vol 91 (1) ◽  
pp. 203-220 ◽  
Author(s):  
Jean-Pierre Demailly
Keyword(s):  
Vector Bundle ◽  
Vanishing Theorems ◽  
Ample Vector Bundle ◽  
Tensor Powers

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.

The positivity of the Chern classes of an ample vector bundle

1971 ◽  
Vol 12 (2) ◽  
pp. 112-117 ◽  
Author(s):  
Spencer Bloch ◽  
David Gieseker
Keyword(s):  
Vector Bundle ◽  
Chern Classes ◽  
Ample Vector Bundle

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.

The threefold containing the Bordiga surface of degree ten as a hyperplane section

2008 ◽  
Vol 145 (3) ◽  
pp. 619-622
Author(s):  
HIDETOSHI MAEDA
Keyword(s):  
Vector Bundle ◽  
Tangent Bundle ◽  
Hyperplane Section ◽  
Ample Vector Bundle ◽  
Rank 2

AbstractLet be a very ample vector bundle of rank 2 on $\Bbb P^2$ with c1() = 4 and c2() = 6. Then it is proved that is the cokernel of a bundle monomorphism $\mathcal O_{\Bbb P^2}(1)^{\oplus 2}\to T_{\Bbb P^2}^{\oplus 2}$, where $T_{\Bbb P^2}$ is the tangent bundle of $\Bbb P^2$. This gives a new example of a threefold containing a Bordiga surface as a hyperplane section.

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.

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