{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/64605"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/64605","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"The moduli space of hypersurfaces whose singular locus has high dimension","abstract":"Fix integers n and b with n =/> 3 and 1 =/< b < n - 1. Let k be an algebraically closed field. Consider the moduli space X of hypersurfaces in P\" of fixed degree I whose singular locus is at least b-dimensional. We prove that for large 1, X has a unique irreducible component of maximal dimension, consisting of the hypersurfaces singular along a linear b-dimensional subspace of P\".","abstract_html":"Fix integers n and b with n =/&gt; 3 and 1 =/&lt; b &lt; n - 1. Let k be an algebraically closed field. Consider the moduli space X of hypersurfaces in P&quot; of fixed degree I whose singular locus is at least b-dimensional. We prove that for large 1, X has a unique irreducible component of maximal dimension, consisting of the hypersurfaces singular along a linear b-dimensional subspace of P&quot;.","abstract_has_math":false,"creators":["Slavov, Kaloyan (Kaloyan Stefanov)"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Bjorn Poonen."],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011","date_published":"2011","updated_at":"2026-07-22T22:21:37Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/64605","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Bjorn Poonen."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Dept. of Mathematics."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. 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They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/64605"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 75)."]},{"key":"dc:description.abstract","label":"Abstract","values":["Fix integers n and b with n =/> 3 and 1 =/< b < n - 1. Let k be an algebraically closed field. Consider the moduli space X of hypersurfaces in P\" of fixed degree I whose singular locus is at least b-dimensional. We prove that for large 1, X has a unique irreducible component of maximal dimension, consisting of the hypersurfaces singular along a linear b-dimensional subspace of P\"."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["The moduli space of hypersurfaces whose singular locus has high dimension"]}]}],"canonical_facts":{"dc:contributor.advisor":["Bjorn Poonen."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Slavov, Kaloyan (Kaloyan Stefanov)"],"dc:date.accessioned":["2011-06-20T15:59:07Z"],"dc:date.available":["2011-06-20T15:59:07Z"],"dc:date.issued":["2011"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 75)."],"dc:description.abstract":["Fix integers n and b with n =/> 3 and 1 =/< b < n - 1. Let k be an algebraically closed field. Consider the moduli space X of hypersurfaces in P\" of fixed degree I whose singular locus is at least b-dimensional. We prove that for large 1, X has a unique irreducible component of maximal dimension, consisting of the hypersurfaces singular along a linear b-dimensional subspace of P\"."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/64605"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["The moduli space of hypersurfaces whose singular locus has high dimension"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:37Z"}