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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 2, Pages 430–441 (Mi izv1720)  

This article is cited in 14 scientific papers (total in 15 papers)

Smoothness of the general anticanonical divisor on a Fano 3-fold

V. V. Shokurov

Abstract: Smoothness of the general anticanonical divisor of a Fano 3-fold is proved. In addition, an analogous result is established for the linear system $|\mathscr H|$, where $r\mathscr H\sim-K_V$ for some natural number $r$. The results obtained in the paper can be used to investigate projective imbeddings of Fano 3-folds.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1980, 14:2, 395–405

Bibliographic databases:

UDC: 513.6
MSC: Primary 14J10; Secondary 14N05, 14M20
Received: 27.04.1978

Citation: V. V. Shokurov, “Smoothness of the general anticanonical divisor on a Fano 3-fold”, Izv. Akad. Nauk SSSR Ser. Mat., 43:2 (1979), 430–441; Math. USSR-Izv., 14:2 (1980), 395–405

Citation in format AMSBIB
\by V.~V.~Shokurov
\paper Smoothness of the general anticanonical divisor on a~Fano 3-fold
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 2
\pages 430--441
\jour Math. USSR-Izv.
\yr 1980
\vol 14
\issue 2
\pages 395--405

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Shokurov, “The existence of a straight line on Fano 3-folds”, Math. USSR-Izv., 15:1 (1980), 173–209  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. 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
    3. Yu. G. Prokhorov, “The existence of a smooth divisor on Fano 4-folds of index 2”, Russian Acad. Sci. Sb. Math., 83:1 (1995), 119–131  mathnet  crossref  mathscinet  zmath  isi
    4. Yu. G. Prokhorov, “On algebraic threefolds whose hyperplane sections are Enriques surfaces”, Sb. Math., 186:9 (1995), 1341–1352  mathnet  crossref  mathscinet  zmath  isi
    5. I. Yu. Fedorov, “Some conic bundles”, Math. Notes, 63:6 (1998), 796–801  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. F. Ambro, “Ladders on Fano varieties”, J Math Sci, 94:1 (1999), 1126  crossref
    7. 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
    8. Priska Jahnke, Thomas Peternell, Ivo Radloff, “Threefolds with big and nef anticanonical bundles I”, Math Ann, 333:3 (2005), 569  crossref  mathscinet  zmath  isi
    9. 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
    10. Priska Jahnke, Ivo Radloff, “Fano threefolds with sections in Ω1V (1)”, Math Nachr, 280:1-2 (2007), 127  crossref  mathscinet  zmath  isi
    11. F. A. Bogomolov, Vik. S. Kulikov, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (obituary)”, Russian Math. Surveys, 64:5 (2009), 939–946  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. Meng Chen, “On anti-pluricanonical systems of ℚ-Fano 3-folds”, Sci. China Math, 2011  crossref
    13. Makiko Mase, “Families of K3 Surfaces in Smooth Fano 3-Folds with Picard Number 2”, Viet J Math, 2014  crossref
    14. Yuri G. Prokhorov, “Rationality of Fano Threefolds with Terminal Gorenstein Singularities. I”, Proc. Steklov Inst. Math., 307 (2019), 210–231  mathnet  crossref  crossref  isi  elib
    15. Birkar C., “Anti-Pluricanonical Systems on Fano Varieties”, Ann. Math., 190:2 (2019), 345–463  crossref  isi
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