dc.contributor.advisor Lang, Jeffrey dc.contributor.author Alkarni, Shalan dc.date.accessioned 2016-11-03T23:08:42Z dc.date.available 2016-11-03T23:08:42Z dc.date.issued 2016-05-31 dc.date.submitted 2016 dc.identifier.other http://dissertations.umi.com/ku:14635 dc.identifier.uri http://hdl.handle.net/1808/21802 dc.description.abstract In 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.extent 60 pages dc.language.iso en dc.publisher University of Kansas dc.rights Copyright held by the author. dc.subject Mathematics dc.subject Algebra dc.subject Algebraic Geometry dc.subject Class Groups dc.subject Commutative Algebra dc.subject Divisors dc.subject Group of Logarithmic Derivatives dc.title Three Dimensional Jacobian Derivations And Divisor Class Groups dc.type Dissertation dc.contributor.cmtemember Mandal, Satyagopal dc.contributor.cmtemember Purnaprajna, Bangere dc.contributor.cmtemember Jiang, Yunfeng dc.contributor.cmtemember Brinton, Jacquelene dc.thesis.degreeDiscipline Mathematics dc.thesis.degreeLevel Ph.D. dc.identifier.orcid dc.rights.accessrights openAccess
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