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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 2, Pages 402–411 (Mi izv1300)  

This article is cited in 8 scientific papers (total in 8 papers)

On correspondences between K3 surfaces

V. V. Nikulin


Abstract: Using arithmetic of integral quadratic forms and results of Mukai, it is proved among other things that an endomorphism over $\mathbf Q$ of the cohomology lattice of a $K3$ surface over $\mathbf C$ preserving the Hodge structure and the intersection form is induced by an algebraic cycle (as was conjectured in [2]) provided that the Picard lattice $S_X$ of the surface $X$ represents zero (in particular, this is so if $\operatorname{rg}S_X\geqslant5$). Previously this result was obtained by Mukai under the assumption that $\operatorname{rg}S_X\geqslant11$.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 30:2, 375–383

Bibliographic databases:

UDC: 512.774+512.734+511.334
MSC: Primary 14J28; Secondary 14C30, 11E12
Received: 03.02.1985

Citation: V. V. Nikulin, “On correspondences between K3 surfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 51:2 (1987), 402–411; Math. USSR-Izv., 30:2 (1988), 375–383

Citation in format AMSBIB
\Bibitem{Nik87}
\by V.~V.~Nikulin
\paper On~correspondences between K3~surfaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 2
\pages 402--411
\mathnet{http://mi.mathnet.ru/izv1300}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=897004}
\zmath{https://zbmath.org/?q=an:0653.14007}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 30
\issue 2
\pages 375--383
\crossref{https://doi.org/10.1070/IM1988v030n02ABEH001018}


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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. C. G. Madonna, V. V. Nikulin, “On a Classical Correspondence between K3 Surfaces”, Proc. Steklov Inst. Math., 241 (2003), 120–153  mathnet  mathscinet  zmath
    2. V. V. Nikulin, “On Correspondences of a K3 Surface with Itself. I”, Proc. Steklov Inst. Math., 246 (2004), 204–226  mathnet  mathscinet  zmath
    3. C. G. Madonna, V. V. Nikulin, “Explicit correspondences of a K3 surface with itself”, Izv. Math., 72:3 (2008), 497–508  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Claudio Pedrini, “The Chow Motive of a K3 Surface”, Milan j math, 2009  crossref  isi
    5. Ulrich Schlickewei, “The Hodge conjecture for self-products of certain K3 surfaces”, Journal of Algebra, 324:3 (2010), 507  crossref
    6. Viacheslav V. Nikulin, “Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups”, Proc. Steklov Inst. Math., 273 (2011), 229–237  mathnet  crossref  mathscinet  zmath  isi  elib
    7. Claudio Pedrini, “On the finite dimensionality of a K3 surface”, manuscripta math, 2011  crossref
    8. Christian Liedtke, “Supersingular K3 surfaces are unirational”, Invent. math, 2014  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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