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Algebraic surfaces with an infinite set of planes of oblique symmetry. II

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Abstract

Suppose that G is an infinite group generated by obliquereflections with respect to hyperplanes in the real spaceE m and that theµ j-planes IIµj = IIdj ⊕ IIγj (j =\(\overline {0,q} \) G(u) -orbits of directions of symmetryu (hyperplanes of symmetry conjugate to vectors IIdj pass throughγ j-planesII γj). A complete solution of the problem of the mutual position of three IIγj is given. Systems of generatrices of the rings of invariants of a series of groups G are found.

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References

  1. V. F. Ignatenko, "Algebraic surfaces with an infinite set of planes of oblique symmetry, I," Ukrain. Geom. Sb., No. 32, 20–39 (1989).

    Google Scholar 

  2. V. F. Ignatenko, The Structure of Invariants of Infinite Groups Generated by Oblique Reflections [in Russian], Simferopol' (1987). Manuscript deposited in Ukrain.NIINTI on July 13, 1987. Dep. No. 1988-Uk.87.

  3. V. F. Ignatenko, "Special algebraic surfaces with an infinite set of planes of oblique symmetry," Ukrain. Geom. Sb., No. 33, 55–61 (1990).

    Google Scholar 

  4. V. F. Ignatenko, Special Algebraic Surfaces With Symmetries [in Russian], Simferopol' (1988). Manuscript deposited in Ukrain.NIINTI on July 5, 1988. Dep. No. 1768-Uk.88.

  5. A. E. Zalesskii, "The fixed algebra of a group generated by reflections is not always free," Arch. Math.,41 434–437 (1983).

    Google Scholar 

  6. V. F. Igantenko, "Invariants of a group generated by oblique reflections inE 11," Ukrain. Geom. Sb., No. 31, 59–62 (1988).

    Google Scholar 

  7. A. E. Veles'ko, "The existence of groups generated by reflections with infinitely generated rings of invariants," Dokl. Akad. Nauk Belorus.SSR,30 No. 2, 105–107 (1986).

    Google Scholar 

  8. J. Dieudonné, J. Carrell, and D. Mumford, Geometric Invariant Theory [Russian translation], Moscow (1974).

  9. V. F. Ignatenko, The Structure of the Invariants of Infinite Groups Generated by Reflections [in Russian], Simferopol' (1986). Manuscript deposited in VINITI August 7, 1986. Dep. No. 5608-B86.

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Authors
  1. V. F. Ignatenko
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Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 42–51, 1991.

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Ignatenko, V.F. Algebraic surfaces with an infinite set of planes of oblique symmetry. II. J Math Sci 69, 854–861 (1994). https://doi.org/10.1007/BF01250814

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  • DOI: https://doi.org/10.1007/BF01250814

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