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Mathematics of the USSR-Sbornik, 1989, Volume 63, Issue 2, Pages 457–482
DOI: https://doi.org/10.1070/SM1989v063n02ABEH003285 (Mi sm1719) 		 
This article is cited in 37 scientific papers (total in 37 papers)

Birational automorphisms of a three-dimensional quartic with a quadratic singularity

A. V. Pukhlikov
English version PDF (1386 kB) Citations (37)
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DOI: https://doi.org/10.1070/SM1989v063n02ABEH003285
Abstract: The author studies birational automorphisms of a hypersurface of degree 4 in the four-dimensional projective space over an algebraically closed field having a unique ordinary double point of general type. It is shown that the group of birational automorphisms of a quartic is a semidirect product of a normal subgroup of finite index freely generated by 25 birational involutions and the (finite) group of biregular (projective) automorphisms of the quartic. Such a quartic is not rational.
The proof is based on the techniques of maximal singularities due to V. A. Iskovskih and Yu. I. Manin.
Bibliography: 7 titles.
Received: 02.12.1986
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1988, Volume 135(177), Number 4, Pages 472–496
Bibliographic databases:
Document Type: Article
UDC: 513.6
MSC: 14E05, 14E35, 14J30, 14M20
Language: English
Original paper language: Russian
Citation: A. V. Pukhlikov, “Birational automorphisms of a three-dimensional quartic with a quadratic singularity”, Mat. Sb. (N.S.), 135(177):4 (1988), 472–496; Math. USSR-Sb., 63:2 (1989), 457–482
Citation in format AMSBIB
\Bibitem{Puk88}
\by A.~V.~Pukhlikov
\paper Birational automorphisms of a three-dimensional quartic with a quadratic singularity
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 135(177)
\issue 4
\pages 472--496
\mathnet{http://mi.mathnet.ru/sm1719}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=942134}
\zmath{https://zbmath.org/?q=an:0668.14007|0655.14006}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 63
\issue 2
\pages 457--482
\crossref{https://doi.org/10.1070/SM1989v063n02ABEH003285}
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  • https://www.mathnet.ru/eng/sm/v177/i4/p472
    • This publication is cited in the following 37 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:359
    Russian version PDF:107
    English version PDF:12
    References:36
    First page:1
     
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