In mathematics, a vectorbundle is a geometrical construct where to every point of a topological space (or manifold, or algebraic variety) we attach a vector space in a compatible way, so that all those vector spaces, "glued together", form another topological space (or manifold or variety).
Vectorbundles are special fiber bundles, loosely speaking those where the fibers are vector spaces.
Smooth vectorbundles are defined by requiring that E and X be smooth manifolds, π: E - X be a smooth map, and the local trivialization maps φ be diffeomorphisms.
Many AMPLE programs were published in Acorn Computers Ltd User magazine.
AMPLE (an abbreviation of Advanced Multi-Purpose LanguagE) is a scripting programming language and a part of the Falcon Framework software framework developed for the Apollo/Domain computer by Mentor Graphics.
As the Apollo/Domain was very popular in computer-aided engineering (especially in electronic design automation), AMPLE is still used in several Mentor Graphics applications such as Design Architect and is only slowly being obsoleted.
Sectional geometric genera for amplevectorbundles, Hironobu Ishihara
Two invariants, called the $c_1$-sectional geometric genus and the $\co(1)$-sectional geometric genus, are introduced for generalized polarized manifolds, i.e., pairs of a projective manifold and an amplevectorbundle on it.
We classify generalized polarized manifolds of the smallest $c_1$ or $\co(1)$-sectional geometric genus under the spannedness condition for amplevectorbundles.
Advances in Geometry(Site not responding. Last check: 2007-10-13)
In this paper, we give two applications of the theory of multiplier ideals to vectorbundles over complex projective manifolds, generalizing to higher rank results already established for line bundles.
The first addresses the existence of sections of (suitable twists) of symmetric powers of a very amplevectorbundle, vanishing on a given subvariety.
The second is a vanishing theorem of Griffiths type, adjusted with an additional multiplier ideal term as in the standard Nadel vanishing theorem.
An algebraic or analytic vectorbundle with an ample sheaf of regular (resp.
analytic) sections (see Ample sheaf; Positive vectorbundle).
eom.springer.de /a/a012150.htm (50 words)
HAL :: BROWSE(Site not responding. Last check: 2007-10-13)
Building on Fujita-Griffiths method of computing metrics on Hodge bundles, we show that the direct image of an adjoint semi-ample line bundle by a projective submersion has a continuous metric with Griffiths semi-positive curvature.
This shows that for every holomorphic semi-ample vectorbundle $E$ on a complex manifold, and every positive integer $k$, the vectorbundle $S^kE\otimes\det E$ has a continuous metric with Griffiths semi-positive curvature.
If $E$ is ample on a projective manifold, the metric can be made smooth and Griffiths positive.
New Preprints in 1995(Site not responding. Last check: 2007-10-13)
ANDREATTA M., MELLA M. - Contractions on a manifold polarized by an amplevectorbundle, Bonn 1994 s.
BODEN H.U. - Rationality of the moduli space of vectorbundles over a smooth curve, Bures-sur-Yvette 1995 s.
ZAGIER D. - On the cohomology of moduli spaces of rank two vectorbundles over curves, Bonn 1995 s.
www.impan.gov.pl /LIB/pr95.html (9943 words)
Articles and manuscripts by Jean-Pierre Demailly(Site not responding. Last check: 2007-10-13)
[27] Vanishing theorems for tensor powers of a positive vectorbundle, Proceedings of the Conference Geometry and Analysis on Manifolds held at Katata, Japan (August 1987), edited by T. Sunada, Lecture Notes in Math.
Peternell and M. Schneider) Compact complex manifolds whose tangent bundles satisfy numerical effectivity properties, Proceedings of the Conference in honour of M.S. Narasimhan and C.S. Seshadri, Tata Institute of Fundamental Research, Bombay, Oxford University Press, Bombay (1995) (dvi)
Peternell and M. Schneider) Compact Kähler manifolds with hermitian semipositive anticanonical bundle, Compositio Math.
Advances in Geometry(Site not responding. Last check: 2007-10-13)
Received February 13, 2001; revised May 21, 2001 and June 25, 2001
Let $\cal E$ be an amplevectorbundle of rank $r$ on a complex projective manifold $X$ such that there exists a section $s \in \Gamma(\cal E)$ whose zero locus, $Z = (s = 0)$, is a smooth submanifold of the expected dimension $\dim X - r$.
We study the problem of extending birational contractions of $Z$ to the ambient variety proving an extension property for blow-ups and we apply our results to classify $X$ as above when $Z$ is a $\proj$-bundle on a surface with nonnegative Kodaira dimension.
