Ample vector bundle characterizations of projective bundles and quadric fibrations over curves

2012 ◽  
Author(s):  
Antonio Lanteri ◽  
Hidetoshi Maeda
Keyword(s):  
Vector Bundle ◽  
Ample Vector Bundle ◽  
Projective Bundles

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 Projective Bundles on Infinite-Dimensional Complex Spaces

2004 ◽  
Vol 11 (1) ◽  
pp. 43-48
Author(s):  
E. Ballico
Keyword(s):  
Banach Space ◽  
Vector Bundle ◽  
Holomorphic Vector Bundle ◽  
Line Bundles ◽  
Holomorphic Line Bundle ◽  
Infinite Dimensional ◽  
Complex Spaces ◽  
Projective Bundles ◽  
Holomorphic Embeddings ◽  
Holomorphic Line Bundles

Abstract Let V be a complex localizing Banach space with countable unconditional basis and E a rank r holomorphic vector bundle on P(V). Here we study the holomorphic embeddings of P(E) into products of projective spaces and the holomorphic line bundles on P(E). In particular we prove that if r ≥ 3, then H 1(P(E), L) = 0 for every holomorphic line bundle L on P(E).

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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