Homological mirror symmetry for a Calabi-Yau hypersurface in projective space
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2012
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| Online Access: | http://hdl.handle.net/1721.1/73374 |
| _version_ | 1826215967233933312 |
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| author | Sheridan, Nicholas (Nicholas James) |
| author2 | Paul Seidel. |
| author_facet | Paul Seidel. Sheridan, Nicholas (Nicholas James) |
| author_sort | Sheridan, Nicholas (Nicholas James) |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. |
| first_indexed | 2024-09-23T16:40:17Z |
| format | Thesis |
| id | mit-1721.1/73374 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T16:40:17Z |
| publishDate | 2012 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/733742019-04-12T09:20:45Z Homological mirror symmetry for a Calabi-Yau hypersurface in projective space Sheridan, Nicholas (Nicholas James) Paul Seidel. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. Cataloged from PDF version of thesis. Includes bibliographical references (p. 365-369). This thesis is concerned with Kontsevich's Homological Mirror Symmetry conjecture. In Chapter 1, which is based on [1], we consider the n-dimensional pair of pants, which is defined to be the complement of n + 2 generic hyperplanes in CPn. The pair of pants is conjectured to be mirror to the Landau-Ginzburg model (Cn+2 , W), where W = z1...zn+2 We construct an immersed Lagrangian sphere in the pair of pants, and show that its endomorphism A.. algebra in the Fukaya category is quasi-isomorphic to the endomorphism dg algebra of the structure sheaf of the origin in the mirror,.giving some evidence for the Homological Mirror Symmetry conjecture in this case. In Chapter 2, which is based on [2], we build on these results to prove Homological Mirror Symmetry for a smooth d-dimensional Calabi-Yau hypersurface in projective space, for any d =/> 3. by Nicholas Sheridan. Ph.D. 2012-09-27T15:26:40Z 2012-09-27T15:26:40Z 2012 2012 Thesis http://hdl.handle.net/1721.1/73374 809688972 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 369 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Sheridan, Nicholas (Nicholas James) Homological mirror symmetry for a Calabi-Yau hypersurface in projective space |
| title | Homological mirror symmetry for a Calabi-Yau hypersurface in projective space |
| title_full | Homological mirror symmetry for a Calabi-Yau hypersurface in projective space |
| title_fullStr | Homological mirror symmetry for a Calabi-Yau hypersurface in projective space |
| title_full_unstemmed | Homological mirror symmetry for a Calabi-Yau hypersurface in projective space |
| title_short | Homological mirror symmetry for a Calabi-Yau hypersurface in projective space |
| title_sort | homological mirror symmetry for a calabi yau hypersurface in projective space |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/73374 |
| work_keys_str_mv | AT sheridannicholasnicholasjames homologicalmirrorsymmetryforacalabiyauhypersurfaceinprojectivespace |