On planar rational cuspidal curves
Massachusetts Institute of Technology. Department of Mathematics.
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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.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.18Cataloged from PDF version of thesis.Includes bibliographical references (pages 145-146).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology