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Enumerative algebraic geometry via techniques of symplectic topology and analysis of local obstructions

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dc.contributor.advisor Tomasz S. Mrowka. en_US
dc.contributor.author Zinger, Aleksey, 1975- en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.date.accessioned 2005-08-23T19:54:37Z
dc.date.available 2005-08-23T19:54:37Z
dc.date.copyright 2002 en_US
dc.date.issued 2002 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/8402
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002. en_US
dc.description Includes bibliographical references (p. 239-240). en_US
dc.description.abstract Enumerative geometry of algebraic varieties is a fascinating field of mathematics that dates back to the nineteenth century. We introduce new computational tools into this field that are motivated by recent progress in symplectic topology and its influence on enumerative geometry. The most straightforward applications of the methods developed are to enumeration of rational curves with a cusp of specified nature in projective spaces. A general approach for counting positive-genus curves with a fixed complex structure is also presented. The applications described include enumeration of rational curves with a (3,4)-cusp, genus-two and genus-three curves with a fixed complex structure in the two-dimensional complex projective space, and genus-two curves with a fixed complex structure in the three-dimensional complex projective space. Our constructions may be applicable to problems in symplectic topology as well. en_US
dc.description.statementofresponsibility by Aleksey Zinger. en_US
dc.format.extent 240 p. en_US
dc.format.extent 18179663 bytes
dc.format.extent 18179423 bytes
dc.format.mimetype application/pdf
dc.format.mimetype application/pdf
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
dc.subject Mathematics. en_US
dc.title Enumerative algebraic geometry via techniques of symplectic topology and analysis of local obstructions en_US
dc.type Thesis en_US
dc.description.degree Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 50595301 en_US


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