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Mathematics of the USSR-Sbornik, 1971, Volume 15, Issue 3, Pages 361–403
DOI: https://doi.org/10.1070/SM1971v015n03ABEH001552
(Mi sm3299)
 

This article is cited in 18 scientific papers (total in 18 papers)

The Noether–Enriques theorem on canonical curves

V. V. Shokurov
References:
Abstract: The principal result of the present work consists in the proof that an intersection of quadrics passing through a canonical curve is a reduced variety. The possible cases when the intersection of quadrics does not coincide with the curve itself are also examined in this article.
Figures: 1.
Bibliography: 8 titles.
Received: 03.11.1970
Bibliographic databases:
Document Type: Article
UDC: 513.015.7
MSC: Primary 14N05; Secondary 15H45, 53A20
Language: English
Original paper language: Russian
Citation: V. V. Shokurov, “The Noether–Enriques theorem on canonical curves”, Math. USSR-Sb., 15:3 (1971), 361–403
Citation in format AMSBIB
\Bibitem{Sho71}
\by V.~V.~Shokurov
\paper The Noether--Enriques theorem on canonical curves
\jour Math. USSR-Sb.
\yr 1971
\vol 15
\issue 3
\pages 361--403
\mathnet{http://mi.mathnet.ru/eng/sm3299}
\crossref{https://doi.org/10.1070/SM1971v015n03ABEH001552}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=337982}
\zmath{https://zbmath.org/?q=an:0225.14017}
Linking options:
  • https://www.mathnet.ru/eng/sm3299
  • https://doi.org/10.1070/SM1971v015n03ABEH001552
  • https://www.mathnet.ru/eng/sm/v128/i3/p367
  • This publication is cited in the following 18 articles:
    1. Bruno Dewer, “Extensions of Gorenstein weighted projective 3-spaces and characterization of the primitive curves of their surface sections”, Math. Z., 309:4 (2025)  crossref
    2. Yu. G. Prokhorov, “Trekhmernye mnogoobraziya Fano”, Lekts. kursy NOTs, 31, MIAN, M., 2022, 3–154  mathnet  crossref
    3. Juan Migliore, Uwe Nagel, “Gorenstein algebras presented by quadrics”, Collect. Math, 64:2 (2013), 211  crossref  mathscinet  zmath
    4. PIETRO DE POI, FRANCESCO ZUCCONI, “FERMAT HYPERSURFACES AND SUBCANONICAL CURVES”, Int. J. Math, 22:12 (2011), 1763  crossref  mathscinet  zmath
    5. 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
    6. C. G. Madonna, V. V. Nikulin, “On a Classical Correspondence between K3 Surfaces”, Proc. Steklov Inst. Math., 241 (2003), 120–153  mathnet  mathscinet  zmath
    7. Nguyen Khac Viet, M. Saito, “On Mordell–Weil lattices for non-hyperelliptic fibrations on surfaces with zero geometric genus and irregularity”, Izv. Math., 66:4 (2002), 789–805  mathnet  crossref  crossref  mathscinet  zmath
    8. David Eisenbud, Sorin Popescu, “The Projective Geometry of the Gale Transform”, Journal of Algebra, 230:1 (2000), 127  crossref  mathscinet  zmath
    9. I. A. Cheltsov, “Bounded three-dimensional Fano varieties of integer index”, Math. Notes, 66:3 (1999), 360–365  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. V. D. Belousov, V. E. Plisko, E. B. Yanovskaya, D. D. Sokolov, S. Yu. Maslov, A. A. Bukhshtab, V. I. Nechaev, V. M. Paskonov, V. A. Artamonov, A. V. Prokhorov, N. V. Efimov, B. V. Khvedelidze, I. V. Dolgachev, V. A. Iskovskikh, A. B. Ivanov, V. T. Bazylev, A. V. Arkhangel'skiǐ, A. A. Sapozhenko, P. S. Saltan, P. S. Soltan, V. A. Chuyanov, M. Sh. Farber, S. V. Shvedenko, V. P. Petrenko, I. P. Mysovskikh, V. A. Trenogin, M. K. Samarin, Yu. A. Kuznetsov, E. D. Solomentsev, M. S. Nikulin, L. D. Kudryavtsev, V. N. Latyshev, D. V. Anosov, A. L. Shmel'kin, L. N. Shevrin, L. V. Kuz'min, V. L. Popov, D. V. Alekseevskiǐ, V. N. Remeslennikov, P. L. Dobrushin, V. V. Prelov, G. S. Khovanskiǐ, A. L. Onishchik, A. K. Tolpygo, L. A. Sidorov, L. A. Bokut', A. Ya. Kiruta, E. A. Palyutin, A. D. Taǐmanov, E. I. Vilkas, V. V. Rumyantsev, E. G. D'yakonov, A. F. Shapkin, L. E. Evtushik, V. I. Sobolev, V. M. Starszhinskiǐ, S. J. Pokhozhaev, V. G. Karmanov, Encyclopaedia of Mathematics, 1995, 67  crossref
    11. M. Hazewinkel, Encyclopaedia of Mathematics, 1990, 361  crossref
    12. Dolgachev I. Ortland D., “Point Sets in Projective Spaces and Theta Functions”, Asterisque, 1988, no. 165, 1–210  mathscinet  isi
    13. V. V. Shokurov, “Prym varieties: theory and applications”, Math. USSR-Izv., 23:1 (1984), 83–147  mathnet  crossref  mathscinet  zmath
    14. Masaaki Homma, “Theorem of Enriques-Petri type for a very ample invertible sheaf on a curve of genus three”, Math Z, 183:3 (1983), 343  crossref
    15. Robert Treger, “On equations defining arithmetically Cohen-Macaulay schemes, II”, Duke Math. J., 48:1 (1981)  crossref
    16. V. A. Iskovskikh, “Fano 3-folds. II”, Math. USSR-Izv., 12:3 (1978), 469–506  mathnet  crossref  mathscinet  zmath
    17. V. A. Iskovskikh, “Fano 3-folds. I”, Math. USSR-Izv., 11:3 (1977), 485–527  mathnet  crossref  mathscinet  zmath
    18. V. V. Nikulin, “An analogue of the Torelli theorem for Kummer surfaces of Jacobians”, Math. USSR-Izv., 8:1 (1974), 21–41  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
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