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Title: Vector Bundles Over Hypersurfaces Of Projective Varieties
Authors: Tripathi, Amit
Advisors: Ghosh, Mrinal K
Keywords: Hypersurfaces
Vector Bundles
Vector Bundle Extensions
Vector Bundle Extension Theorem
Noether-Lefschetz Theorem
Vector Bundles on Ellipitic Curves
Grothendieck-Lefschetz Theory
Grothendieck-Lefschetz Theorem
Submitted Date: Jul-2012
Series/Report no.: G25245
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 non-singular projective variety, extends as a vector bundle to an open set containing that ample divisor. Our method is to follow the general Groethendieck-Lefschetz 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 Noether-Lefschetz theorems by Joshi and Ravindra-Srinivas. In the last part of the thesis, we make a specific study of vector bundles over elliptic curve.
Abstract file URL: http://etd.ncsi.iisc.ernet.in/abstracts/2981/G25245-Abs.pdf
URI: http://etd.iisc.ernet.in/handle/2005/2318
Appears in Collections:Mathematics (math)

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