{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/90190"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/90190","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"On planar rational cuspidal curves","abstract":"This thesis studies rational curves in the complex projective plane that are homeomorphic to their normalizations. We derive some combinatorial constraints on such curves from a result of Borodzik-Livingston in Heegaard-Floer homology. Using these constraints and other tools from algebraic geometry, we offer a solution to certain cases of the Coolidge-Nagata problem on the rectifiability of planar rational cuspidal curves, that is, their equivalence to lines under the Cremona group of birational automorphisms of the plane.","abstract_html":"This thesis studies rational curves in the complex projective plane that are homeomorphic to their normalizations. We derive some combinatorial constraints on such curves from a result of Borodzik-Livingston in Heegaard-Floer homology. Using these constraints and other tools from algebraic geometry, we offer a solution to certain cases of the Coolidge-Nagata problem on the rectifiability of planar rational cuspidal curves, that is, their equivalence to lines under the Cremona group of birational automorphisms of the plane.","abstract_has_math":false,"creators":["Liu, Tiankai"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mathematics.","school":null,"contributors":[],"advisors":["James McKernan."],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-22T22:21:28Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. 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