Complex crystallographic groups I

Syoshi TOKUNAGA; Masaaki YOSHIDA

doi:10.2969/jmsj/03440581

Syoshi TOKUNAGA, Masaaki YOSHIDA

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JOURNAL FREE ACCESS

1982 Volume 34 Issue 4 Pages 581-593

DOI https://doi.org/10.2969/jmsj/03440581

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Published: 1982 Received: November 20, 1980 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 : 1) M. A. Armstrong, On the fundamental group of an orbit space, Proc. Cambridge Philos. Soc., 61 (1965), 639-646.
2) H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic groups of four-dimensional space, John Wiley & Sons, 1978.
3) C. Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math., 77 (1955), 778-782.
4) A. M. Cohen, Finite complex reflection groups, Ann. Sci. École Norm. Sup., 9 (1976), 379-436.
5) H. S. M. Coxeter, Regular complex polytopes, Cambridge Univ. Press, 1974.
6) D. W. Crowe, Some two dimensional unitary groups generated by three reflections, Canad. J. Math., 13 (1961), 418-426.
7) L. Flatto, Invariants of finite reflection groups, L'enseignement mathématique II^e serie, 24 (1978), 237-292.
8) S. Hattori and M. Yoshida, Local theory of Fuchsian systems with certain discrete monodromy groups III, Funkcial. Ekvac., 22 (1979), 1-40.
9) S. Iitaka, Algebraic geometry I, II, III, Iwanami, 1977.
10) J. Kaneko, S. Tokunaga and M. Yoshida, Complex crystallographic groups II, J. Math. Soc. Japan, 34 (1982), 595-605.
11) G. C. Shephard, Abstract definitions for reflection groups, Canad. J. Math., 9 (1957), 273-276.
12) G.C. Shephard and I.A. Todd, Finite unitary reflection groups, Canad. J. Math., 6 (1954), 274-304.
13) O. V. Shvartsman, Chevalley's theorem for complex crystallographic groups generated by reflections in the affine space C², Uspehi Mat. Nauk, 34 (1979), 249-250. Translation: Russian Math. Surveys, 34 (1979), 239-240.
14) T. Suwa, Compact quotient spaces of C² by affine transformation groups, J. Differential Geometry, 19 (1975), 239-252.
15) K. Uchida and H. Yoshihara, Discontinuous groups of affine transformations of C³, Tohoku Math. J., 28 (1976), 89-94.
16) J. A. Wolf, Spaces of constant curvature, McGraw-Hill, 1967.
17) H. Yoshihara, On deformations of hyperelliptic manifolds, Proc. Internat. Symp. on Algebraic Geometry, Kyoto, 1977, 735-737.

Right : [1] M. A. Armstrong, On the fundamental group of an orbit space, Proc. Cambridge Philos. Soc., 61 (1965), 639-646.
[2] H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic groups of four-dimensional space, John Wiley & Sons, 1978.
[3] C. Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math., 77 (1955), 778-782.
[4] A. M. Cohen, Finite complex reflection groups, Ann. Sci. École Norm. Sup., 9 (1976), 379-436.
[5] H. S. M. Coxeter, Regular complex polytopes, Cambridge Univ. Press, 1974.
[6] D. W. Crowe, Some two dimensional unitary groups generated by three reflections, Canad. J. Math., 13 (1961), 418-426.
[7] L. Flatto, Invariants of finite reflection groups, L'enseignement mathématique II^e serie, 24 (1978), 237-292.
[8] S. Hattori and M. Yoshida, Local theory of Fuchsian systems with certain discrete monodromy groups III, Funkcial. Ekvac., 22 (1979), 1-40.
[9] S. Iitaka, Algebraic geometry I, II, III, Iwanami, 1977.
[10] J. Kaneko, S. Tokunaga and M. Yoshida, Complex crystallographic groups II, J. Math. Soc. Japan, 34 (1982), 595-605.
[11] G. C. Shephard, Abstract definitions for reflection groups, Canad. J. Math., 9 (1957), 273-276.
[12] G. C. Shephard and I.A. Todd, Finite unitary reflection groups, Canad. J. Math., 6 (1954), 274-304.
[13] O. V. Shvartsman, Chevalley's theorem for complex crystallographic groups generated by reflections in the affine space C², Uspehi Mat. Nauk, 34 (1979), 249-250. Translation: Russian Math. Surveys, 34 (1979), 239-240.
[14] T. Suwa, Compact quotient spaces of C² by affine transformation groups, J. Differential Geometry, 19 (1975), 239-252.
[15] K. Uchida and H. Yoshihara, Discontinuous groups of affine transformations of C³, Tohoku Math. J., 28 (1976), 89-94.
[16] J. A. Wolf, Spaces of constant curvature, McGraw-Hill, 1967.
[17] H. Yoshihara, On deformations of hyperelliptic manifolds, Proc. Internat. Symp. on Algebraic Geometry, Kyoto, 1977, 735-737.

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