| 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 w1p = f, w2p = 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 Zp, is never trivial, and is generated by those hyperplane sections whose forms are factors of linear combinations of f and g. |
