Proceedings of the Japan Academy, Series A, Mathematical Sciences

Multiplicative excellent family of type $E_{6}$

Tetsuji Shioda

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Abstract

We show that the equation (1) in the text defines a multiplicative excellent family of elliptic surfaces (or of cubic surfaces) with Galois group isomorphic to the Weyl group of type $E_{6}$. The main properties of the family are formulated as Theorems 1 and 2 in § 3.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 88, Number 3 (2012), 46-51.

Dates
First available in Project Euclid: 5 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.pja/1330958576

Digital Object Identifier
doi:10.3792/pjaa.88.46

Mathematical Reviews number (MathSciNet)
MR2409500

Zentralblatt MATH identifier
1297.14042

Subjects
Primary: 11S05: Polynomials 12F12: Inverse Galois theory 14J27: Elliptic surfaces

Keywords
Weyl group cubic surface Mordell-Weil lattices

Citation

Shioda, Tetsuji. Multiplicative excellent family of type $E_{6}$. Proc. Japan Acad. Ser. A Math. Sci. 88 (2012), no. 3, 46--51. doi:10.3792/pjaa.88.46. https://projecteuclid.org/euclid.pja/1330958576


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