Elliptic Fibrations on a Generic Jacobian Kummer Surface
We describe all the elliptic fibrations with section on the Kummer surface X of the Jacobian of a very general curve C of genus 2 over an algebraically closed field of characteristic 0, modulo the automorphism group of X and the symmetric group on the Weierstrass points of C. In particular, we compu...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Mathematical Society (AMS)
2015
|
| Online Access: | http://hdl.handle.net/1721.1/93124 |
| _version_ | 1826193935753543680 |
|---|---|
| author | Kumar, Abhinav |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kumar, Abhinav |
| author_sort | Kumar, Abhinav |
| collection | MIT |
| description | We describe all the elliptic fibrations with section on the Kummer surface X of the Jacobian of a very general curve C of genus 2 over an algebraically closed field of characteristic 0, modulo the automorphism group of X and the symmetric group on the Weierstrass points of C. In particular, we compute elliptic parameters and Weierstrass equations for the 25 different fibrations and analyze the reducible fibers and Mordell-Weil lattices. This answers completely a question posed by Kuwata and Shioda in 2008. |
| first_indexed | 2024-09-23T09:47:37Z |
| format | Article |
| id | mit-1721.1/93124 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:47:37Z |
| publishDate | 2015 |
| publisher | American Mathematical Society (AMS) |
| record_format | dspace |
| spelling | mit-1721.1/931242022-09-30T16:52:22Z Elliptic Fibrations on a Generic Jacobian Kummer Surface Kumar, Abhinav Massachusetts Institute of Technology. Department of Mathematics Kumar, Abhinav We describe all the elliptic fibrations with section on the Kummer surface X of the Jacobian of a very general curve C of genus 2 over an algebraically closed field of characteristic 0, modulo the automorphism group of X and the symmetric group on the Weierstrass points of C. In particular, we compute elliptic parameters and Weierstrass equations for the 25 different fibrations and analyze the reducible fibers and Mordell-Weil lattices. This answers completely a question posed by Kuwata and Shioda in 2008. National Science Foundation (U.S.) (Grant DMS-0757765) National Science Foundation (U.S.) (Grant DMS-0952486) Solomon Buchsbaum AT&T Research Fund 2015-01-22T16:24:49Z 2015-01-22T16:24:49Z 2014-05 2012-02 Article http://purl.org/eprint/type/JournalArticle 1056-3911 1534-7486 http://hdl.handle.net/1721.1/93124 Kumar, Abhinav en_US http://www.ams.org/journals/jag/2014-23-04/S1056-3911-2014-00620-2/ Journal of Algebraic Geometry Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf American Mathematical Society (AMS) arXiv |
| spellingShingle | Kumar, Abhinav Elliptic Fibrations on a Generic Jacobian Kummer Surface |
| title | Elliptic Fibrations on a Generic Jacobian Kummer Surface |
| title_full | Elliptic Fibrations on a Generic Jacobian Kummer Surface |
| title_fullStr | Elliptic Fibrations on a Generic Jacobian Kummer Surface |
| title_full_unstemmed | Elliptic Fibrations on a Generic Jacobian Kummer Surface |
| title_short | Elliptic Fibrations on a Generic Jacobian Kummer Surface |
| title_sort | elliptic fibrations on a generic jacobian kummer surface |
| url | http://hdl.handle.net/1721.1/93124 |
| work_keys_str_mv | AT kumarabhinav ellipticfibrationsonagenericjacobiankummersurface |