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This article is cited in 12 scientific papers (total in 12 papers)
On algebraic cycles on a fibre product of families of K3-surfaces
O. V. Nikol'skaya Vladimir State University
Abstract:
We prove the Hodge conjecture and the standard conjecture of Lefschetz
type for fibre squares of smooth projective non-isotrivial families
of $\mathrm K3$-surfaces over a smooth projective curve under the assumption
that the rank of the lattice of transcendental cycles on a generic geometric
fibre of the family is an odd prime. We prove the Hodge conjecture for
a fibre product of two non-isotrivial families of $\mathrm K3$-surfaces
(possibly with degenerations) under the condition that, for every point
of the curve, at least one family has non-singular fibre over this point,
and the rank of the lattice of transcendental cycles on a generic geometric
fibre of one family is odd and not equal to the corresponding rank
for the other.
Keywords:
Hodge conjecture, standard conjecture of Lefschetz type, $\mathrm K3$-surface.
Received: 28.11.2011
Citation:
O. V. Nikol'skaya, “On algebraic cycles on a fibre product of families of K3-surfaces”, Izv. RAN. Ser. Mat., 77:1 (2013), 145–164; Izv. Math., 77:1 (2013), 143–162
Linking options:
https://www.mathnet.ru/eng/im7939https://doi.org/10.1070/IM2013v077n01ABEH002631 https://www.mathnet.ru/eng/im/v77/i1/p145
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Abstract page: | 586 | Russian version PDF: | 189 | English version PDF: | 10 | References: | 73 | First page: | 25 |
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