{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"K\u00e4hler potentials on the Moduli space of stable parabolic bundles over the Riemann sphere","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/76406"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"We start this work by reinterpreting the Moduli problem of stable parabolic bundles from a complex analytic perspective. This allows us to introduce canonical complex coordinates on the Moduli space, analogous to the Bers' coordinates on Teichm\u00fcller spaces. Similarly, a suitable analog of uniformization will play a central role. Finally, the identification of the tangent space at a point with a certain space of automorphic forms leads to the introduction of the parabolic Narasimhan-Atiyah-Bott metric on the Moduli space, which is analogous to the Weil-Petersson metric. Secondly, for each stable parabolic bundle, a regularized WZNW action functional is defined on the space of singular Hermitian metrics with prescribed asymptotics at a finite set of points in the sphere. We prove that these functionals evaluated at their extrema gives rise to a function on the Moduli space that is a K\u00e4hler potential for the parabolic Narasimhan-Atiyah-Bott metric over a certain analytic open subset."},{"label":"dcterms.available","value":"2017-09-20T16:50:10Z"},{"label":"dcterms.contributor","value":"Kra, Irwin."},{"label":"dcterms.creator","value":"Meneses-Torres, Claudio"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:50:10Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:50:10Z"},{"label":"dcterms.description","value":"Department of Mathematics."},{"label":"dcterms.extent","value":"107 pg."},{"label":"dcterms.format","value":"Application/PDF"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/76406"},{"label":"dcterms.issued","value":"2013-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:50:10Z (GMT). No. of bitstreams: 1\nMenesesTorres_grad.sunysb_0771E_11570.pdf: 864746 bytes, checksum: fe68f7576e1d246019b4db229de13b32 (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Mathematics"},{"label":"dcterms.title","value":"K\u00e4hler potentials on the Moduli space of stable parabolic bundles over the Riemann sphere"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/59%2F57%2F20%2F59572089521398237699042739299909106784/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/59%2F57%2F20%2F59572089521398237699042739299909106784","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}