On Algebraic Cycles on Fibre Products of Non-isotrivial Families of Regular Surfaces with Geometric Genus 1
https://doi.org/10.18255/1818-1015-2016-4-440-465
Abstract
Let 
) be a projective family of surfaces (possibly with degenerations) over a smooth projective curve . Assume that the discriminant loci 
are disjoint,
for any smooth fibre and the period map associated with the variation of Hodge structures 
(where 
is a smooth part of the morphism ), is non-constant. If for generic geometric fibres 
and the following conditions hold: (i) 
is an odd integer; (ii) , then for any smooth projective model of the fibre product 
the Hodge conjecture on algebraic cycles is true. If, besides, the morphisms are smooth, 
are odd prime numbers and , then for
) be a projective family of surfaces (possibly with degenerations) over a smooth projective curve . Assume that the discriminant loci are disjoint, for any smooth fibre and the period map associated with the variation of Hodge structures (where is a smooth part of the morphism ), is non-constant. If for generic geometric fibres and the following conditions hold: (i) is an odd integer; (ii) , then for any smooth projective model of the fibre product the Hodge conjecture on algebraic cycles is true. If, besides, the morphisms are smooth, are odd prime numbers and , then for
Keywords
Supporting agencies: Russian Foundation for basic research under the Grant No 16-31-00266
About the Author
O. V. Nikol’skaya
A.G. and N.G. Stoletov Vladimir State University, Vladimir
Russian Federation
Russian Federation
Nikol’skaya Olga Vladimirovna, PhD
A.G. and N.G. Stoletov Vladimir State University, Gorky str., 87, Vladimir, 600000
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Review
For citations:
Nikol’skaya O.V. On Algebraic Cycles on Fibre Products of Non-isotrivial Families of Regular Surfaces with Geometric Genus 1. Modeling and Analysis of Information Systems. 2016;23(4):440-465. (In Russ.) https://doi.org/10.18255/1818-1015-2016-4-440-465
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