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dc.contributor.advisorLang, Jeffrey
dc.contributor.authorAlkarni, Shalan
dc.date.accessioned2016-11-03T23:08:42Z
dc.date.available2016-11-03T23:08:42Z
dc.date.issued2016-05-31
dc.date.submitted2016
dc.identifier.otherhttp://dissertations.umi.com/ku:14635
dc.identifier.urihttp://hdl.handle.net/1808/21802
dc.description.abstractIn this thesis, we use P. Samuel's purely inseparable descent methods to investigate the divisor class groups of the intersections of pairs of hypersurfaces of the form $w_1^p=f$, $w_2^p=g$ in affine $5$-space with $f$, $g$ in $A=k[x,y,z]$; $k$ is an algebraically closed field of characteristic $p$ $$ $0$. This corresponds to studying the divisor class group of the kernels of three dimensional Jacobian derivations on $A$ that are regular in codimension one. Our computations focus primarily on pairs where $f$, $g$ are quadratic forms. We find results concerning the order and the type of these groups. We show that the divisor class group is a direct sum of up to three copies of $\mathbb{Z}_p$, is never trivial, and is generated by those hyperplane sections whose forms are factors of linear combinations of $f$ and $g$.
dc.format.extent60 pages
dc.language.isoen
dc.publisherUniversity of Kansas
dc.rightsCopyright held by the author.
dc.subjectMathematics
dc.subjectAlgebra
dc.subjectAlgebraic Geometry
dc.subjectClass Groups
dc.subjectCommutative Algebra
dc.subjectDivisors
dc.subjectGroup of Logarithmic Derivatives
dc.titleThree Dimensional Jacobian Derivations And Divisor Class Groups
dc.typeDissertation
dc.contributor.cmtememberMandal, Satyagopal
dc.contributor.cmtememberPurnaprajna, Bangere
dc.contributor.cmtememberJiang, Yunfeng
dc.contributor.cmtememberBrinton, Jacquelene
dc.thesis.degreeDisciplineMathematics
dc.thesis.degreeLevelPh.D.
dc.identifier.orcid
dc.rights.accessrightsopenAccess


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