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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 $\operatorname{rg}S_X\geqslant11$.
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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
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\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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This publication is cited in the following articles:
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C. G. Madonna, V. V. Nikulin, “On a Classical Correspondence between K3 Surfaces”, Proc. Steklov Inst. Math., 241 (2003), 120–153
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V. V. Nikulin, “On Correspondences of a K3 Surface with Itself. I”, Proc. Steklov Inst. Math., 246 (2004), 204–226
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C. G. Madonna, V. V. Nikulin, “Explicit correspondences of a K3 surface with itself”, Izv. Math., 72:3 (2008), 497–508
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Claudio Pedrini, “The Chow Motive of a K3 Surface”, Milan j math, 2009
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Ulrich Schlickewei, “The Hodge conjecture for self-products of certain K3 surfaces”, Journal of Algebra, 324:3 (2010), 507
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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
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Claudio Pedrini, “On the finite dimensionality of a K3 surface”, manuscripta math, 2011
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Christian Liedtke, “Supersingular K3 surfaces are unirational”, Invent. math, 2014
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