etd@IISc Collection:http://hdl.handle.net/2005/412016-10-24T18:52:27Z2016-10-24T18:52:27ZVector Bundles Over Hypersurfaces Of Projective VarietiesTripathi, Amithttp://hdl.handle.net/2005/23182014-06-02T05:08:47Z2014-06-01T18:30:00ZTitle: Vector Bundles Over Hypersurfaces Of Projective Varieties
Authors: Tripathi, Amit
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.2014-06-01T18:30:00ZUncertainty Handling In Knowledge-Based Systems Via Evidence RepresentationSrinivas, Nowdurihttp://hdl.handle.net/2005/18892013-01-18T10:20:03Z2013-01-17T18:30:00ZTitle: Uncertainty Handling In Knowledge-Based Systems Via Evidence Representation
Authors: Srinivas, Nowduri2013-01-17T18:30:00ZTime Series Analysis Of Neurobiological SignalsHariharan, Nhttp://hdl.handle.net/2005/14522011-09-28T06:54:18Z2011-09-27T18:30:00ZTitle: Time Series Analysis Of Neurobiological Signals
Authors: Hariharan, N2011-09-27T18:30:00ZA Study On Solutions Of Singular Integral EquationsGeorge, A Jhttp://hdl.handle.net/2005/17362012-05-31T07:57:41Z2012-05-30T18:30:00ZTitle: A Study On Solutions Of Singular Integral Equations
Authors: George, A J2012-05-30T18:30:00Z