On planar rational cuspidal curves
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
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| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2014
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| Online Access: | http://hdl.handle.net/1721.1/90190 |
| _version_ | 1826200366791786496 |
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| author | Liu, Tiankai |
| author2 | James McKernan. |
| author_facet | James McKernan. Liu, Tiankai |
| author_sort | Liu, Tiankai |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014. |
| first_indexed | 2024-09-23T11:35:18Z |
| format | Thesis |
| id | mit-1721.1/90190 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T11:35:18Z |
| publishDate | 2014 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/901902019-04-12T12:49:57Z On planar rational cuspidal curves Liu, Tiankai James McKernan. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014. 18 Cataloged from PDF version of thesis. Includes bibliographical references (pages 145-146). 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. by Tiankai Liu. Ph. D. 2014-09-19T21:45:04Z 2014-09-19T21:45:04Z 2014 2014 Thesis http://hdl.handle.net/1721.1/90190 890211671 eng 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. http://dspace.mit.edu/handle/1721.1/7582 146 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Liu, Tiankai On planar rational cuspidal curves |
| title | On planar rational cuspidal curves |
| title_full | On planar rational cuspidal curves |
| title_fullStr | On planar rational cuspidal curves |
| title_full_unstemmed | On planar rational cuspidal curves |
| title_short | On planar rational cuspidal curves |
| title_sort | on planar rational cuspidal curves |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/90190 |
| work_keys_str_mv | AT liutiankai onplanarrationalcuspidalcurves |