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Mat. Sb., 2014, Volume 205, Number 2, Pages 123–130 (Mi msb8267)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00097
Dynasty Foundation


DOI: https://doi.org/10.4213/sm8267

Full text: PDF file (499 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:2, 269–276

Bibliographic databases:

UDC: 512.7+512.72+512.725
MSC: 43C30
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

Citation in format AMSBIB
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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. O. V. Nikolskaya, “Ob algebraicheskikh tsiklakh na rassloennykh proizvedeniyakh neizotrivialnykh semeistv regulyarnykh poverkhnostei s geometricheskim rodom 1”, Model. i analiz inform. sistem, 23:4 (2016), 440–465  mathnet  crossref  mathscinet  elib
    2. O. V. Oreshkina, “O gipotezakh Khodzha, Teita i Mamforda–Teita dlya rassloennykh proizvedenii semeistv regulyarnykh poverkhnostei s geometricheskim rodom 1”, Model. i analiz inform. sistem, 25:3 (2018), 312–322  mathnet  crossref  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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