Orbifold points on Teichmüller curves and Jacobians with complex multiplication
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2011
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| Online Access: | http://hdl.handle.net/1721.1/67810 |
| _version_ | 1826216013893468160 |
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| author | Mukamel, Ronen E. (Ronen Eliahu) |
| author2 | Curtis T. McMullen. |
| author_facet | Curtis T. McMullen. Mukamel, Ronen E. (Ronen Eliahu) |
| author_sort | Mukamel, Ronen E. (Ronen Eliahu) |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011. |
| first_indexed | 2024-09-23T16:40:56Z |
| format | Thesis |
| id | mit-1721.1/67810 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T16:40:56Z |
| publishDate | 2011 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/678102019-04-12T11:21:33Z Orbifold points on Teichmüller curves and Jacobians with complex multiplication Odbifold points and Jacobians with complex multiplication on Teichmüller curves in genus two Mukamel, Ronen E. (Ronen Eliahu) Curtis T. McMullen. 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, 2011. Cataloged from PDF version of thesis. Includes bibliographical references (p. 83-85). For each integer D >/= 5 with D =/- 0 or 1 mod 4, the Weierstrass curve WD is an algebraic curve and a finite volume hyperbolic orbifold which admits an algebraic and isometric immersion into the moduli space of genus two Riemann surfaces. The Weierstrass curves are the main examples of Teichmüller curves in genus two. The primary goal of this thesis is to determine the number and type of orbifold points on each component of WD. Our enumeration of the orbifold points, together with [Ba] and [Mc3], completes the determination of the homeomorphism type of WD and gives a formula for the genus of its components. We use our formula to give bounds on the genus of WD and determine the Weierstrass curves of genus zero. We will also give several explicit descriptions of each surface labeled by an orbifold point on WD. by Ronen E. Mukamel. Ph.D. 2011-12-19T19:00:32Z 2011-12-19T19:00:32Z 2011 2011 Thesis http://hdl.handle.net/1721.1/67810 767907868 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 85 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Mukamel, Ronen E. (Ronen Eliahu) Orbifold points on Teichmüller curves and Jacobians with complex multiplication |
| title | Orbifold points on Teichmüller curves and Jacobians with complex multiplication |
| title_full | Orbifold points on Teichmüller curves and Jacobians with complex multiplication |
| title_fullStr | Orbifold points on Teichmüller curves and Jacobians with complex multiplication |
| title_full_unstemmed | Orbifold points on Teichmüller curves and Jacobians with complex multiplication |
| title_short | Orbifold points on Teichmüller curves and Jacobians with complex multiplication |
| title_sort | orbifold points on teichmuller curves and jacobians with complex multiplication |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/67810 |
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