Open Access
March 2012 Multiplicative excellent family of type $E_{6}$
Tetsuji Shioda
Proc. Japan Acad. Ser. A Math. Sci. 88(3): 46-51 (March 2012). DOI: 10.3792/pjaa.88.46


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.


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Tetsuji Shioda. "Multiplicative excellent family of type $E_{6}$." Proc. Japan Acad. Ser. A Math. Sci. 88 (3) 46 - 51, March 2012.


Published: March 2012
First available in Project Euclid: 5 March 2012

zbMATH: 1297.14042
MathSciNet: MR2409500
Digital Object Identifier: 10.3792/pjaa.88.46

Primary: 11S05 , 12F12 , 14J27

Keywords: cubic surface , Mordell-Weil lattices , Weyl group

Rights: Copyright © 2012 The Japan Academy

Vol.88 • No. 3 • March 2012
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