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dc.contributor.advisorGhosh, Mrinal K
dc.contributor.authorTripathi, Amit
dc.date.accessioned2014-06-02T05:08:47Z
dc.date.accessioned2018-07-31T06:09:00Z
dc.date.available2014-06-02T05:08:47Z
dc.date.available2018-07-31T06:09:00Z
dc.date.issued2014-06-02
dc.date.submitted2012-07
dc.identifier.urihttp://etd.iisc.ac.in/handle/2005/2318
dc.identifier.abstracthttp://etd.iisc.ac.in/static/etd/abstracts/2981/G25245-Abs.pdfen_US
dc.description.abstractIn 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.en_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesG25245en_US
dc.subjectHypersurfacesen_US
dc.subjectVector Bundlesen_US
dc.subjectVector Bundle Extensionsen_US
dc.subjectVector Bundle Extension Theoremen_US
dc.subjectNoether-Lefschetz Theoremen_US
dc.subjectVector Bundles on Ellipitic Curvesen_US
dc.subjectGrothendieck-Lefschetz Theoryen_US
dc.subjectGrothendieck-Lefschetz Theoremen_US
dc.subject.classificationTopologyen_US
dc.titleVector Bundles Over Hypersurfaces Of Projective Varietiesen_US
dc.typeThesisen_US
dc.degree.namePhDen_US
dc.degree.levelDoctoralen_US
dc.degree.disciplineFaculty of Scienceen_US


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