{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/29352"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/29352","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Towards characterizing morphims between high dimensional hypersurfaces","abstract":"This thesis is organized into two papers. All results are proven over an algebraically closed field of characteristic zero. Paper 1 concerns morphisms between hypersurfaces in Pn, n =/> 4. We show that if the two hypersurfaces involved in the morphism are of general type, then the morphism of hypersurfaces extends to an everywhere-defined endomorphism of Pn. A corollary is that if X [right arrow] Y is a nonconstant morphism of hypersurfaces of large dimension and large degree, then deg Y divides deg X. The main tool used to analyze morphism between hypersurfaces is an inequality of Chern classes analogous to the Hurwitz-inequality. Paper 2 is a long example. We check that every morphism from a quintic hypersurface in I4 to a nonsingular cubic hypersurface in P4 is constant. In the process, we classify morphisms froin the projective plane to nonsingular cubic threefolds.","abstract_html":"This thesis is organized into two papers. All results are proven over an algebraically closed field of characteristic zero. Paper 1 concerns morphisms between hypersurfaces in Pn, n =/> 4. We show that if the two hypersurfaces involved in the morphism are of general type, then the morphism of hypersurfaces extends to an everywhere-defined endomorphism of Pn. A corollary is that if X [right arrow] Y is a nonconstant morphism of hypersurfaces of large dimension and large degree, then deg Y divides deg X. The main tool used to analyze morphism between hypersurfaces is an inequality of Chern classes analogous to the Hurwitz-inequality. Paper 2 is a long example. We check that every morphism from a quintic hypersurface in I4 to a nonsingular cubic hypersurface in P4 is constant. In the process, we classify morphisms froin the projective plane to nonsingular cubic threefolds.","abstract_has_math":false,"creators":["Sheppard, David C. (David Christopher), 1977-"],"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":["Aise Johan de Jong."],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003","date_published":"2003","updated_at":"2026-07-22T22:21:42Z","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/1721.1/29352","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Aise Johan de Jong."]},{"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. Dept. of Mathematics."]},{"key":"dc:creator","label":"Author","values":["Sheppard, David C. 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A corollary is that if X [right arrow] Y is a nonconstant morphism of hypersurfaces of large dimension and large degree, then deg Y divides deg X. The main tool used to analyze morphism between hypersurfaces is an inequality of Chern classes analogous to the Hurwitz-inequality. Paper 2 is a long example. We check that every morphism from a quintic hypersurface in I4 to a nonsingular cubic hypersurface in P4 is constant. In the process, we classify morphisms froin the projective plane to nonsingular cubic threefolds."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Towards characterizing morphims between high dimensional hypersurfaces"]}]}],"canonical_facts":{"dc:contributor.advisor":["Aise Johan de Jong."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Sheppard, David C. (David Christopher), 1977-"],"dc:date.accessioned":["2005-10-14T20:01:18Z"],"dc:date.available":["2005-10-14T20:01:18Z"],"dc:date.issued":["2003"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.","Includes bibliographical references (p. 44)."],"dc:description.abstract":["This thesis is organized into two papers. All results are proven over an algebraically closed field of characteristic zero. Paper 1 concerns morphisms between hypersurfaces in Pn, n =/> 4. We show that if the two hypersurfaces involved in the morphism are of general type, then the morphism of hypersurfaces extends to an everywhere-defined endomorphism of Pn. A corollary is that if X [right arrow] Y is a nonconstant morphism of hypersurfaces of large dimension and large degree, then deg Y divides deg X. The main tool used to analyze morphism between hypersurfaces is an inequality of Chern classes analogous to the Hurwitz-inequality. Paper 2 is a long example. We check that every morphism from a quintic hypersurface in I4 to a nonsingular cubic hypersurface in P4 is constant. In the process, we classify morphisms froin the projective plane to nonsingular cubic threefolds."],"dc:description.degree":["Ph.D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/1721.1/29352"],"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. 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