Algebraic homology classes on algebraic varieties

In this paper, the relation between the algebraic homology classes on a protective algebraic variety and on its “general” hyperplane section is studied. It is proved in particular that on a “general” section of an algebraic variety $V$ by a hypersurface of sufficiently high degree, any algebraic homology class, taken with some multiplicity, is cut by some algebraic homology class of the variety $V$.