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dc.contributor.advisorGross, Benedict H.
dc.contributor.authorThorne, Jack A.
dc.date.accessioned2012-08-10T20:34:38Z
dc.date.issued2012-08-10
dc.date.submitted2012
dc.identifier.citationThorne, Jack A. 2012. The Arithmetic of Simple Singularities. Doctoral dissertation, Harvard University.en_US
dc.identifier.otherhttp://dissertations.umi.com/gsas.harvard:10339en
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:9396425
dc.description.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.en_US
dc.description.sponsorshipMathematicsen_US
dc.language.isoen_USen_US
dash.licenseLAA
dc.subjectmathematicsen_US
dc.titleThe Arithmetic of Simple Singularitiesen_US
dc.typeThesis or Dissertationen_US
dash.depositing.authorThorne, Jack A.
dc.date.available2012-08-10T20:34:38Z
thesis.degree.date2012en_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorHarvard Universityen_US
thesis.degree.leveldoctoralen_US
thesis.degree.namePh.D.en_US
dash.contributor.affiliatedThorne, Jack


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