The tautological classes of the moduli spaces of stable maps to flag varieties
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2006
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| Online Access: | http://hdl.handle.net/1721.1/31164 |
| _version_ | 1826190079337431040 |
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| author | Oprea, Dragos Nicolae |
| author2 | Gang Tian. |
| author_facet | Gang Tian. Oprea, Dragos Nicolae |
| author_sort | Oprea, Dragos Nicolae |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005. |
| first_indexed | 2024-09-23T08:34:42Z |
| format | Thesis |
| id | mit-1721.1/31164 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T08:34:42Z |
| publishDate | 2006 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/311642022-01-13T07:54:35Z The tautological classes of the moduli spaces of stable maps to flag varieties Oprea, Dragos Nicolae Gang Tian. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Department of Mathematics Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005. Includes bibliographical references (p. 113-116). 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. by Dragos Nicolae Oprea. Ph.D. 2006-02-02T18:54:27Z 2006-02-02T18:54:27Z 2005 2005 Thesis http://hdl.handle.net/1721.1/31164 61214689 eng 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 116 p. 7707064 bytes 7721205 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Oprea, Dragos Nicolae The tautological classes of the moduli spaces of stable maps to flag varieties |
| title | The tautological classes of the moduli spaces of stable maps to flag varieties |
| title_full | The tautological classes of the moduli spaces of stable maps to flag varieties |
| title_fullStr | The tautological classes of the moduli spaces of stable maps to flag varieties |
| title_full_unstemmed | The tautological classes of the moduli spaces of stable maps to flag varieties |
| title_short | The tautological classes of the moduli spaces of stable maps to flag varieties |
| title_sort | tautological classes of the moduli spaces of stable maps to flag varieties |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/31164 |
| work_keys_str_mv | AT opreadragosnicolae thetautologicalclassesofthemodulispacesofstablemapstoflagvarieties AT opreadragosnicolae tautologicalclassesofthemodulispacesofstablemapstoflagvarieties |