On the geometry of a smooth model of a fibre product of families of K3 surfaces

The Hodge conjecture on algebraic cycles is proved for a smooth projective model of a fibre product of nonisotrivial 1-parameter families of K3 surfaces (possibly with degeneracies) over a smooth projective curve under the assumption that, for generic geometric fibres and , the ring is an imaginary...

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Bibliographic Details
Published in:Sbornik. Mathematics 2014-01, Vol.205 (2), p.269-276
Main Author: Nikol'skaya, O. V.
Format: Article
Language:English
Subjects:
Algebra
Curves (geometry)
DIAGRAMS
FIBERS
Fibre
Fibres
Fields (mathematics)
GEOMETRY
Hodge conjecture
K3 surface
MATHEMATICAL METHODS AND COMPUTING
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
Number theory
SURFACES
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Summary:The Hodge conjecture on algebraic cycles is proved for a smooth projective model of a fibre product of nonisotrivial 1-parameter families of K3 surfaces (possibly with degeneracies) over a smooth projective curve under the assumption that, for generic geometric fibres and , the ring is an imaginary quadratic field, , and is a totally real field or else . Bibliography: 10 titles.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM2014v205n02ABEH004374