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Mathematics of the USSR-Sbornik, 1971, Volume 15, Issue 1, Pages 141–166
DOI: https://doi.org/10.1070/SM1971v015n01ABEH001536 (Mi sm3288) 		 
This article is cited in 158 scientific papers (total in 160 papers)

Three-dimensional quartics and counterexamples to the Lüroth problem

V. A. Iskovskikh, Yu. I. Manin
English version PDF (1568 kB) Citations (160) Russian version article
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DOI: https://doi.org/10.1070/SM1971v015n01ABEH001536
Abstract: In this paper we prove that any birational mapping between smooth hypersurfaces of degree four is an isomorphism. Since B. Segre constructed examples of smooth unirational quartics, this leads to a negative resolution of the three-dimensioal Lüroth problem.
Bibliography: 13 titles.
Received: 02.06.1971
Bibliographic databases:
Document Type: Article
UDC: 513.015.7
MSC: 14E05, 14J10
Language: English
Original paper language: Russian
Citation: V. A. Iskovskikh, Yu. I. Manin, “Three-dimensional quartics and counterexamples to the Lüroth problem”, Math. USSR-Sb., 15:1 (1971), 141–166
Citation in format AMSBIB
\Bibitem{IskMan71}
\by V.~A.~Iskovskikh, Yu.~I.~Manin
\paper Three-dimensional quartics and counterexamples to the L\"uroth problem
\jour Math. USSR-Sb.
\yr 1971
\vol 15
\issue 1
\pages 141--166
\mathnet{http://mi.mathnet.ru//eng/sm3288}
\crossref{https://doi.org/10.1070/SM1971v015n01ABEH001536}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=291172}
\zmath{https://zbmath.org/?q=an:03351777|03394301}
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  • https://www.mathnet.ru/eng/sm/v128/i1/p140
    • This publication is cited in the following 160 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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