| dc.contributor.advisor | James McKernan. | en_US |
| dc.contributor.author | Liu, Tiankai | en_US |
| dc.contributor.other | Massachusetts Institute of Technology. Department of Mathematics. | en_US |
| dc.date.accessioned | 2014-09-19T21:45:04Z | |
| dc.date.available | 2014-09-19T21:45:04Z | |
| dc.date.copyright | 2014 | en_US |
| dc.date.issued | 2014 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1721.1/90190 | |
| dc.description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014. | en_US |
| dc.description | 18 | en_US |
| dc.description | Cataloged from PDF version of thesis. | en_US |
| dc.description | Includes bibliographical references (pages 145-146). | en_US |
| dc.description.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. | en_US |
| dc.description.statementofresponsibility | by Tiankai Liu. | en_US |
| dc.format.extent | 146 pages | en_US |
| dc.language.iso | eng | en_US |
| dc.publisher | Massachusetts Institute of Technology | en_US |
| 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. | en_US |
| dc.rights.uri | http://dspace.mit.edu/handle/1721.1/7582 | en_US |
| dc.subject | Mathematics. | en_US |
| dc.title | On planar rational cuspidal curves | en_US |
| dc.type | Thesis | en_US |
| dc.description.degree | Ph. D. | en_US |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | |
| dc.identifier.oclc | 890211671 | en_US |
