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Mat. Sb. (N.S.), 1972, Volume 88(130), Number 1(5), Pages 31–37 (Mi msb3144)  

This article is cited in 9 scientific papers (total in 10 papers)

Birational properties of a surface of degree 4 in $\mathbf P^4_k$

V. A. Iskovskikh


Abstract: It is proved that a smooth surface of fourth degree in $\mathbf P^4_k$, defined over a perfect field $k$, is not birationally isomorphic, over $k$, to the projective plane $\mathbf P^2_k$ if it is $k$-minimal.
Bibliography: 5 titles.

Full text: PDF file (720 kB)
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English version:
Mathematics of the USSR-Sbornik, 1972, 17:1, 30–36

Bibliographic databases:

UDC: 513.015.7
MSC: 14E05, 14J25, 14M20
Received: 31.03.1971

Citation: V. A. Iskovskikh, “Birational properties of a surface of degree 4 in $\mathbf P^4_k$”, Mat. Sb. (N.S.), 88(130):1(5) (1972), 31–37; Math. USSR-Sb., 17:1 (1972), 30–36

Citation in format AMSBIB
\Bibitem{Isk72}
\by V.~A.~Iskovskikh
\paper Birational properties of a~surface of degree~4 in~$\mathbf P^4_k$
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 88(130)
\issue 1(5)
\pages 31--37
\mathnet{http://mi.mathnet.ru/msb3144}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=299606}
\zmath{https://zbmath.org/?q=an:0244.14005|0253.14002}
\transl
\jour Math. USSR-Sb.
\yr 1972
\vol 17
\issue 1
\pages 30--36
\crossref{https://doi.org/10.1070/SM1972v017n01ABEH001489}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. I. Manin, M. A. Tsfasman, “Rational varieties: algebra, geometry and arithmetic”, Russian Math. Surveys, 41:2 (1986), 51–116  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. A. Iskovskikh, S. L. Tregub, “On birational automorphysms of rational surfaces”, Math. USSR-Izv., 38:2 (1992), 251–275  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. A. Iskovskikh, “Factorization of birational maps of rational surfaces from the viewpoint of Mori theory”, Russian Math. Surveys, 51:4 (1996), 585–652  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. A. I. Kostrikin, V. S. Kulikov, Yu. I. Manin, V. V. Nikulin, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, A. N. Tyurin, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (on his 60th birthday)”, Russian Math. Surveys, 54:4 (1999), 863–868  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. I. A. Cheltsov, “Rationality of an Enriques–Fano threefold of genus five”, Izv. Math., 68:3 (2004), 607–618  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Hyperelliptic and trigonal Fano threefolds”, Izv. Math., 69:2 (2005), 365–421  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. Josef Schicho, “The parametric degree of a rational surface”, Math Z, 254:1 (2006), 185  crossref  mathscinet  zmath  isi
    8. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
    9. Prokhorov Yu. Shramov C., “Finite Groups of Birational Selfmaps of Threefolds”, Math. Res. Lett., 25:3 (2018), 957–972  crossref  mathscinet  zmath  isi
    10. J.-L. Colliot-Thélène, “Stably rational surfaces over a quasi-finite field”, Izv. RAN. Ser. matem., 83:3 (2019), 113–126  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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