Show simple item record

dc.contributor.advisorPreviato, Emmaen_US
dc.contributor.authorThompson, Benjamin L.en_US
dc.date.accessioned2021-06-15T17:39:57Z
dc.date.available2021-06-15T17:39:57Z
dc.date.issued2021
dc.identifier.urihttps://hdl.handle.net/2144/42677
dc.description.abstractFor nearly three centuries mathematicians have been interested in polygons which simultaneously circumscribe and inscribe quadrics. They have shown in many contexts (real, complex, non-euclidean, higher dimensional, etc.) that such polygons may be ``rotated'' while maintaining their circum-inscribed quality. Of particular interest has been conditions on the quadrics which guarantee the existence of such polygons. In 1854 Arthur Cayley provided conditions for closure general to polygons of any size in the complex projective plane. We show that under suitable circumstances the curve, defined by Cayley's conditions, on a fibration of Jacobians over the space of families of quadrics is a reducible curve, particularly in genus two. We may infer additional information about points of finite order on the Jacobians based on the component of the reducible curve in which they lie. Using this information we are able to accomplish two tasks. First we provide sufficient closure conditions for Poncelet's Great Theorem in which each vertex of the polygon lies on a distinct quadric. Next, for a polygon circum-inscribed in quadrics in ℙ^3, we provide additional sufficient conditions for closure beyond what mathematicians had previously believed to be necessary and sufficient.en_US
dc.language.isoen_US
dc.rightsAttribution-NonCommercial-ShareAlike 4.0 Internationalen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/
dc.subjectMathematicsen_US
dc.subjectElliptic curveen_US
dc.subjectJacobianen_US
dc.subjectPonceleten_US
dc.titlePoncelet-type theorems and points of finite order on a curve in its Jacobianen_US
dc.typeThesis/Dissertationen_US
dc.date.updated2021-06-09T01:08:39Z
etd.degree.nameDoctor of Philosophyen_US
etd.degree.leveldoctoralen_US
etd.degree.disciplineMathematics & Statisticsen_US
etd.degree.grantorBoston Universityen_US
dc.identifier.orcid0000-0003-0758-8620


This item appears in the following Collection(s)

Show simple item record

Attribution-NonCommercial-ShareAlike 4.0 International
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-ShareAlike 4.0 International