Multiplicative excellent families of elliptic surfaces of type E[subscript 7] or E[subscript 8]
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Kumar_Multiplicative excellent.pdf
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Author(s)
Kumar, Abhinav
Shioda, Tetsuji
Date Issued
2013
Journal
Algebra & Number Theory
Publisher
Mathematical Sciences Publishers
Citation
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.
Version
Author's final manuscript
Abstract
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]).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.2140/ant.2013.7.1613
