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On planar rational cuspidal curves

Author(s)
Liu, Tiankai
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Massachusetts Institute of Technology. Department of Mathematics.
Advisor
James McKernan.
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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
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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.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
 
18
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (pages 145-146).
 
Date issued
2014
URI
http://hdl.handle.net/1721.1/90190
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

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