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 | |