{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"The Degree of Irrationality of Very General Hypersurfaces in Some Homogeneous Spaces","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/11401/78191"},{"label":"dc.language.iso","value":"en_US"},{"label":"dcterms.abstract","value":"The degree of irrationality of an n-dimensional algebraic variety X is the minimal degree of a rational map from X to Pn. The degree of irrationality is a birational invariant with the purpose of measuring how far X is from being rational. For example the degree of irrationality of X is 1 if and only if X is rational. While the invariant has a very classical appearance, it has not attracted very much attention until very recently in [BDPE+15] where it was shown that the degree of irrationality of a very general degree d hypersurface in Pn+1 is d?1, if d is sufficiently large. The method of proof involves relating the geometry of a low degree map to projective space to the geometry of lines in projective space. In this dissertation we show that these methods can be extended to compute the degree of irrationality of hypersurfaces in other rational homogeneous spaces: quadrics, Grassmannians, and products of projective spaces. In particular, we relate the geometry of low degree maps from hypersurfaces in these rational homogeneous spaces to the geometry of lines inside these rational homegeneous spaces. These computations represent some of the first computations of the degree of irrationality for higher dimensional varieties."},{"label":"dcterms.available","value":"2018-03-22T22:39:16Z"},{"label":"dcterms.contributor","value":"Arbarello, Enrico."},{"label":"dcterms.creator","value":"Stapleton, David"},{"label":"dcterms.dateAccepted","value":"2018-03-22T22:39:16Z"},{"label":"dcterms.dateSubmitted","value":"2018-03-22T22:39:16Z"},{"label":"dcterms.description","value":"Department of Mathematics."},{"label":"dcterms.extent","value":"63 pg."},{"label":"dcterms.format","value":"Monograph"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/78191"},{"label":"dcterms.issued","value":"2017-08-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2018-03-22T22:39:16Z (GMT). No. of bitstreams: 1\nStapleton_grad.sunysb_0771E_13351.pdf: 1092518 bytes, checksum: 1570a30b381daac58cb6902d1ef589f0 (MD5)\n  Previous issue date: 2017-08-01"},{"label":"dcterms.subject","value":"Complex Geometry"},{"label":"dcterms.title","value":"The Degree of Irrationality of Very General Hypersurfaces in Some Homogeneous Spaces"},{"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/2/85%2F70%2F70%2F85707052640320420581613641513578529410/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/2/85%2F70%2F70%2F85707052640320420581613641513578529410","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}