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The tautological classes of the moduli spaces of stable maps to flag varieties

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dc.contributor.advisor Gang Tian. en_US Oprea, Dragos Nicolae en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2006-02-02T18:54:27Z 2006-02-02T18:54:27Z 2005 en_US 2005 en_US
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005. en_US
dc.description Includes bibliographical references (p. 113-116). en_US
dc.description.abstract We study the tautological classes of the Kontsevich-Manin moduli spaces of genus 0 stable maps to SL flag varieties. We prove that the rational cohomology and rational Chow rings of these spaces are isomorphic and that they are generated by tautological classes. In the case when the target is a projective space, we present a second proof of this result in the spirit of Gromov-Witten theory by making use of a suitable torus action. In addition, we explicitly describe a Bialynicki-Birula stratification of the Kontsevich-Manin spaces in terms of the Gathmann-Li spaces of relative stable morphisms. Finally, we analyze the small codimension classes on the space of maps to arbitrary flag varieties. We obtain an explicit description of the Picard groups. We formulate a conjecture about relations between the tautological generators, which we check in low codimension. en_US
dc.description.statementofresponsibility by Dragos Nicolae Oprea. en_US
dc.format.extent 116 p. en_US
dc.format.extent 7707064 bytes
dc.format.extent 7721205 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.subject Mathematics. en_US
dc.title The tautological classes of the moduli spaces of stable maps to flag varieties en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 61214689 en_US

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