The versal deformation of the E6-singularity and a family of cubic surfaces

Jiro SEKIGUCHI

doi:10.2969/jmsj/04620355

The versal deformation of the E₆-singularity and a family of cubic surfaces

Jiro SEKIGUCHI

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JOURNAL FREE ACCESS

1994 Volume 46 Issue 2 Pages 355-383

DOI https://doi.org/10.2969/jmsj/04620355

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Published: 1994 Received: February 12, 1993 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : [B] N. Bourbaki, Groupes et Algèbres de Lie, Chaps. 4, 5, 6, Herman, Paris, 1968.
[C] A. Cayley, A memoir on cubic surfaces, Collected Papers VI.
[DO] 1. Dolgachev and D. Ortland, Point sets in projective spaces and theta functions, Astérisque, 165, 1988.
[H] B. Hunt, A remarkable quintic fourfold in P⁵ and its dual variety (Update: 7.1. 1992), in preparation.
[MSY] K. Matsumoto, T. Sasaki and M. Yoshida, The monodromy of the period map of a 4-parameter family of K3 surfaces and the hypergeometric function of type (3, 6), international J. of Math., 3 (1992), 1-164.
[N] I. Naruki, Cross ratio variety as a moduli space of cubic surfaces, Proc. London Math. Soc., 45 (1982), 1-30.
[NS] 1. Naruki and J. Sekiguchi, A modification of Cayley's family of cubic surfaces and birational action of W(E₆) over it, Proc. Japan Acad. Ser. A, 56 (1980), 122-125.
[Se] J. Sekiguchi, The configuration space of 6 points in P², the moduli space of cubic surfaces and the Weyl group of type W(E₆), RIMS Kokyuroku, 848 (1993), 74-85.
[Sh] T. Shioda, Construction of elliptic curves with high rank via the invariants of the Weyl groups, J. Math. Soc. Japan, 43 (1991), 673-719.
[Sl] P. Slodowy, Simple singularities and simple algebraic groups, Lecture Notes in Math., 815.
[T] T. Terada, Fonction hypergéométriques F₁ et fonctions automorphes I, J. Math., Soc. Japan, 35 (1983), 451-475.

Right : [B] N. Bourbaki, Groupes et Algèbres de Lie, Chaps. 4, 5, 6, Herman, Paris, 1968.
[C] A. Cayley, A memoir on cubic surfaces, Collected Papers VI.
[DO] I. Dolgachev and D. Ortland, Point sets in projective spaces and theta functions, Astérisque, 165, 1988.
[H] B. Hunt, A remarkable quintic fourfold in P⁵ and its dual variety (Update: 7.1. 1992), in preparation.
[MSY] K. Matsumoto, T. Sasaki and M. Yoshida, The monodromy of the period map of a 4-parameter family of K3 surfaces and the hypergeometric function of type (3, 6), International J. of Math., 3 (1992), 1-164.
[N] I. Naruki, Cross ratio variety as a moduli space of cubic surfaces, Proc. London Math. Soc., 45 (1982), 1-30.
[NS] I. Naruki and J. Sekiguchi, A modification of Cayley's family of cubic surfaces and birational action of W(E₆) over it, Proc. Japan Acad. Ser. A, 56 (1980), 122-125.
[Se] J. Sekiguchi, The configuration space of 6 points in P², the moduli space of cubic surfaces and the Weyl group of type W(E₆), RIMS Kokyuroku, 848 (1993), 74-85.
[Sh] T. Shioda, Construction of elliptic curves with high rank via the invariants of the Weyl groups, J. Math. Soc. Japan, 43 (1991), 673-719.
[Sl] P. Slodowy, Simple singularities and simple algebraic groups, Lecture Notes in Math., 815.
[T] T. Terada, Fonction hypergéométriques F₁ et fonctions automorphes I, J. Math., Soc. Japan, 35 (1983), 451-475.

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