{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Affine stratifications and equivariant vector bundles on the moduli of principally polarized abelian varieties","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/11401/76388"},{"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 explicitly construct a locally closed affine stratification of the coarse moduli space of principally polarized abelian four folds A4 over the complex numbers and using the work of Roth and Vakil, produce an upper bound for the coherent cohomological dimension and the constructible cohomological dimension of A4. Based on the work of Oort and Van Der Geer, we make a conjecture on the cohomological dimension of the moduli stack Ag for all g. In the second part of the thesis we study the ring of equivariant vector bundles on Ag and study the chern character map from this ring to the tautological ring of Ag. We give a conjectural representation theoretic interpretation of the tautological ring of Ag as a shifted quotient of the representation ring of GL(g,C) by the representation ring of Sp(2g,C)."},{"label":"dcterms.available","value":"2017-09-20T16:50:09Z"},{"label":"dcterms.contributor","value":"Grushevsky, Samuel"},{"label":"dcterms.creator","value":"Atyam, Anant"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:50:09Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:50:09Z"},{"label":"dcterms.description","value":"Department of Mathematics."},{"label":"dcterms.extent","value":"78 pg."},{"label":"dcterms.format","value":"Application/PDF"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/76388"},{"label":"dcterms.issued","value":"2014-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:50:09Z (GMT). No. of bitstreams: 1\nAtyam_grad.sunysb_0771E_11940.pdf: 428933 bytes, checksum: 2b47ebd2666fb94ba197c66cbf08d1b3 (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Abelian Varieties"},{"label":"dcterms.title","value":"Affine stratifications and equivariant vector bundles on the moduli of principally polarized abelian varieties"},{"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/2/15%2F71%2F09%2F157109319009693013271975051366450076183/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/2/15%2F71%2F09%2F157109319009693013271975051366450076183","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}