Multiplicative excellent families of elliptic surfaces of type E[subscript 7] or E[subscript 8]
We describe explicit multiplicative excellent families of rational elliptic surfaces with Galois group isomorphic to the Weyl group of the root lattices E[subscript 7] or E[subscript 8]. The Weierstrass coefficients of each family are related by an invertible polynomial transformation to the generat...
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| Format: | Article |
| Language: | en_US |
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Mathematical Sciences Publishers
2015
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| Online Access: | http://hdl.handle.net/1721.1/92955 |
| _version_ | 1826197381440339968 |
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| author | Kumar, Abhinav Shioda, Tetsuji |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kumar, Abhinav Shioda, Tetsuji |
| author_sort | Kumar, Abhinav |
| collection | MIT |
| description | We describe explicit multiplicative excellent families of rational elliptic surfaces with Galois group isomorphic to the Weyl group of the root lattices E[subscript 7] or E[subscript 8]. The Weierstrass coefficients of each family are related by an invertible polynomial transformation to the generators of the multiplicative invariant ring of the associated Weyl group, given by the fundamental characters of the corresponding Lie group. As an application, we give examples of elliptic surfaces with multiplicative reduction and all sections defined over Q for most of the entries of fiber configurations and Mordell–Weil lattices described by Oguiso and Shioda, as well as examples of explicit polynomials with Galois group W(E[subscript 7]) or W(E[subscript 8]). |
| first_indexed | 2024-09-23T10:47:09Z |
| format | Article |
| id | mit-1721.1/92955 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:47:09Z |
| publishDate | 2015 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | mit-1721.1/929552022-09-27T14:57:28Z Multiplicative excellent families of elliptic surfaces of type E[subscript 7] or E[subscript 8] Kumar, Abhinav Shioda, Tetsuji Massachusetts Institute of Technology. Department of Mathematics Kumar, Abhinav We describe explicit multiplicative excellent families of rational elliptic surfaces with Galois group isomorphic to the Weyl group of the root lattices E[subscript 7] or E[subscript 8]. The Weierstrass coefficients of each family are related by an invertible polynomial transformation to the generators of the multiplicative invariant ring of the associated Weyl group, given by the fundamental characters of the corresponding Lie group. As an application, we give examples of elliptic surfaces with multiplicative reduction and all sections defined over Q for most of the entries of fiber configurations and Mordell–Weil lattices described by Oguiso and Shioda, as well as examples of explicit polynomials with Galois group W(E[subscript 7]) or W(E[subscript 8]). National Science Foundation (U.S.) (Career Grant DMS-0952486) Solomon Buchsbaum AT&T Research Fund 2015-01-20T15:25:41Z 2015-01-20T15:25:41Z 2013 2012-12 Article http://purl.org/eprint/type/JournalArticle 1944-7833 1937-0652 http://hdl.handle.net/1721.1/92955 Kumar, Abhinav, and Tetsuji Shioda. “Multiplicative Excellent Families of Elliptic Surfaces of Type E[subscript 7] or E[subscript 8] .” Algebra & Number Theory 7, no. 7 (2013): 1613–1641. en_US http://dx.doi.org/10.2140/ant.2013.7.1613 Algebra & Number Theory Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Mathematical Sciences Publishers arXiv |
| spellingShingle | Kumar, Abhinav Shioda, Tetsuji Multiplicative excellent families of elliptic surfaces of type E[subscript 7] or E[subscript 8] |
| title | Multiplicative excellent families of elliptic surfaces of type E[subscript 7] or E[subscript 8] |
| title_full | Multiplicative excellent families of elliptic surfaces of type E[subscript 7] or E[subscript 8] |
| title_fullStr | Multiplicative excellent families of elliptic surfaces of type E[subscript 7] or E[subscript 8] |
| title_full_unstemmed | Multiplicative excellent families of elliptic surfaces of type E[subscript 7] or E[subscript 8] |
| title_short | Multiplicative excellent families of elliptic surfaces of type E[subscript 7] or E[subscript 8] |
| title_sort | multiplicative excellent families of elliptic surfaces of type e subscript 7 or e subscript 8 |
| url | http://hdl.handle.net/1721.1/92955 |
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