Vector Bundles Over Hypersurfaces Of Projective Varieties
Abstract
In this thesis we study some questions related to vector bundles over hypersurfaces. More precisely, for hypersurfaces of dimension ≥ 2, we study the extension problem of vector bundles. We find some cohomological conditions under which a vector bundle over an ample divisor of nonsingular projective variety, extends as a vector bundle to an open set containing that ample divisor.
Our method is to follow the general GroethendieckLefschetz theory by showing that a vector bundle extension exists over various thickenings of the ample divisor.
For vector bundles of rank > 1, we find two separate cohomological conditions on vector bundles which shows the extension to an open set containing the ample divisor. For the case of line bundles, our method unifies and recovers the generalized NoetherLefschetz theorems by Joshi and RavindraSrinivas.
In the last part of the thesis, we make a specific study of vector bundles over elliptic curve.
Collections
 Mathematics (MA) [136]
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