Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
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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/1721.1/34551 |
| _version_ | 1826212898283716608 |
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| author | Solomon, Jake P. (Jake Philip) |
| author2 | Gang Tian. |
| author_facet | Gang Tian. Solomon, Jake P. (Jake Philip) |
| author_sort | Solomon, Jake P. (Jake Philip) |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006. |
| first_indexed | 2024-09-23T15:40:12Z |
| format | Thesis |
| id | mit-1721.1/34551 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T15:40:12Z |
| publishDate | 2006 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/345512019-04-12T09:19:03Z Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions Solomon, Jake P. (Jake Philip) Gang Tian. 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, 2006. Includes bibliographical references (p. 107-109). We define a new family of open Gromov-Witten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold arises as the fixed points of an anti-symplectic involution and has dimension 2 or 3. In the strongly semi-positive genus 0 case, the new invariants coincide with Welschinger's invariant counts of real pseudoholomorphic curves. Furthermore, we calculate the new invariant for the real quintic threefold in genus 0 and degree 1 to be 30. The techniques we introduce lay the groundwork for verifying predictions of mirror symmetry for the real quintic. by Jake P. Solomon. Ph.D. 2006-11-07T12:54:46Z 2006-11-07T12:54:46Z 2006 2006 Thesis http://hdl.handle.net/1721.1/34551 71016011 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 109 p. 4324877 bytes 4330908 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Solomon, Jake P. (Jake Philip) Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions |
| title | Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions |
| title_full | Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions |
| title_fullStr | Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions |
| title_full_unstemmed | Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions |
| title_short | Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions |
| title_sort | intersection theory on the moduli space of holomorphic curves with lagrangian boundary conditions |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/34551 |
| work_keys_str_mv | AT solomonjakepjakephilip intersectiontheoryonthemodulispaceofholomorphiccurveswithlagrangianboundaryconditions |