The Arithmetic of Simple Singularities
MetadataShow full item record
CitationThorne, Jack A. 2012. The Arithmetic of Simple Singularities. Doctoral dissertation, Harvard University.
AbstractWe investigate some arithmetic orbit problems in representations of linear algebraic groups arising from Vinberg theory. We aim to give a description of the orbits in these representations using methods with an emphasis on representation theory rather than algebraic geometry, in contrast to previous works of other authors. It turns out that for the representations we consider, the orbits are related to the arithmetic of the Jacobians of certain algebraic curves, which appear as the smooth nearby ﬁbers of deformations of simple singularities. We calculate these families of algebraic curves, and show that the 2-torsion in their Jacobians is canonically identiﬁed with the stabilizers of certain orbits in the corresponding representations.
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:9396425
- FAS Theses and Dissertations