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This article is cited in 2 scientific papers (total in 2 papers)
On the geometry of a smooth model of a fibre product of families of K3 surfaces
O. V. Nikol'skaya Vladimir State University
Abstract:
The Hodge conjecture on algebraic cycles is proved for a smooth projective model $X$ of a fibre product $X_1\times_C X_2$ of nonisotrivial 1-parameter families of K3 surfaces (possibly with degeneracies) $X_{k} \to C$ ($k=1,2$) over a smooth projective curve $C$ under the assumption that, for generic geometric fibres $X_{1s}$ and $ X_{2s}$, the ring $\operatorname{End}_{\operatorname{Hg}(X_{1s})}\operatorname{NS}_{\mathbb Q}(X_{1s})^{\perp}$ is an imaginary quadratic field, $\operatorname{rank}\operatorname{NS}(X_{1s})\neq 18$, and $\operatorname{End}_{\operatorname{Hg}(X_{2s})}\operatorname{NS}_{\mathbb Q}(X_{2s})^{\perp}$ is a totally real field or else $\operatorname{rank}\operatorname{NS}(X_{1s}) < \operatorname{rank}\operatorname{NS}(X_{2s})$.
Bibliography: 10 titles.
Keywords:
Hodge conjecture, K3 surface.
Received: 28.06.2013
Citation:
O. V. Nikol'skaya, “On the geometry of a smooth model of a fibre product of families of K3 surfaces”, Mat. Sb., 205:2 (2014), 123–130; Sb. Math., 205:2 (2014), 269–276
Linking options:
https://www.mathnet.ru/eng/sm8267https://doi.org/10.1070/SM2014v205n02ABEH004374 https://www.mathnet.ru/eng/sm/v205/i2/p123
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Abstract page: | 413 | Russian version PDF: | 148 | English version PDF: | 4 | References: | 56 | First page: | 46 |
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