This article is cited in 2 papers

On Algebraic Cohomology Classes on a Smooth Model of a Fiber Product of Families of K3 surfaces

O. V. Nikol'skaya

Vladimir State University

Abstract: Hodge's conjecture on algebraic cycles is proved for a smooth projective model $X$ of the fiber product $X_1\times_CX_2$ of nonisotrivial one-parameter families of K3 surfaces (possibly with degeneracies) under certain constraints on the ranks of the transcendental cycle lattices of the general geometric fibers $X_{ks}$ and representations of the Hodge groups $\operatorname{Hg}(X_{ks})$.

Keywords: Hodge's conjecture on algebraic cycles, K3 surface, smooth projective model.

UDC: 512.73

Received: 07.06.2013
Revised: 07.04.2014

DOI: 10.4213/mzm10337

 English version: Mathematical Notes, 2014, 96:5, 745–752

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