{"@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 Kontsevich Space of Rational Curves on Cyclic Covers of Projective Space","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/11401/76409"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"In this thesis we consider the space of rational curves on a smooth cyclic cover of Pn. These varieties are the simplest examples of Fano varieties beyond the classical examples of complete intersections in homogeneous spaces. We show that for a general cyclic cover, the Kontsevich moduli stack of stable curves in X is irreducible and has the expected dimension. Specifically, let X be a general smooth cyclic cover of Pn of degree r branched over a divisor of degree rd, and let M(X,e) be the Kontsevich moduli stack of stable rational curves of degree e on X. We show that if 2d(r-1)<n then this space is irreducible with the expected dimension e(n-(r-1)d+1) +n -3 +k."},{"label":"dcterms.available","value":"2017-09-20T16:50:11Z"},{"label":"dcterms.contributor","value":"Grushevsky, Samuel"},{"label":"dcterms.creator","value":"Smith, Lloyd"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:50:11Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:50:11Z"},{"label":"dcterms.description","value":"Department of Mathematics."},{"label":"dcterms.extent","value":"55 pg."},{"label":"dcterms.format","value":"Application/PDF"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/76409"},{"label":"dcterms.issued","value":"2014-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:50:11Z (GMT). No. of bitstreams: 1\nSmith_grad.sunysb_0771E_11732.pdf: 463538 bytes, checksum: 6bcc6f52cfaf1e43073460823d4e03d4 (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":"The Kontsevich Space of Rational Curves on Cyclic Covers of Projective Space"},{"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/2/71%2F69%2F56%2F7169569808206910840285836162801697260/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/2/71%2F69%2F56%2F7169569808206910840285836162801697260","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}