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Real rational curves of low degree

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dc.contributor.advisor Viro, Oleg en_US
dc.contributor.author DMello, Shane en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2017-09-20T16:50:09Z
dc.date.available 2017-09-20T16:50:09Z
dc.date.issued 2013-12-01 en_US
dc.identifier.uri http://hdl.handle.net/11401/76391 en_US
dc.description 56 pgs en_US
dc.description.abstract In the first part of the talk we will consider real planar rational curves of degree 4. We will prove that the rigid isotopy classification of real rational curves of degree 4 in the projective plane can be solved by considering their chord diagrams. In the second part of the talk, we will consider real rational knots on the 3-sphere. The 3-sphere can be realized as a subvariety of the projective space of dimension 4. Real rational knots in the 3-sphere are curves in the 4-dimensional projective space that lie on the 3-sphere. We will prove a rigid isotopy classification of all real rational knots of degrees 6. We will also prove methods of constructing examples of real rational knots of a given degree. The rigid isotopy classification of real rational knots in the projective space is known up to degree 5. We will partially extend this result by classifying real rational knots of degree 6 with four double points, in the projective space. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics en_US
dc.title Real rational curves of low degree en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Starr, Jason en_US
dc.contributor.committeemember Sullivan, Dennis en_US
dc.contributor.committeemember Rocek, Martin en_US

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