In this thesis, we study the ring of differential operators D and the holonomic D-modules on an affine, monomial curve. We obtain an explicit description of the ring of differential operators, the associated graded ring and the module of derivations. We also classify all graded, holonomic, indecomposable D-modules. See thesis abstract for more details.
This thesis was submitted for the degree Doctor Scientiarum in mathematics at the Department of Mathematics, University of Oslo on April 26th 2000. Professor Olav Arnfinn Laudal was the thesis supervisor.
The thesis was defended on June 16th 2000, before the following scientific committee: Professor Jan-Erik Bjørk, University of Stockholm, Professor Valentin Lychagin, University of Tromsø, and Assistant professor Arne B. Sletsjøe, University of Oslo. A doctoral lecture was also presented for the committe. The committe accepted the defense for the degree Doctor Scientarium.