Geodesic
Algebraic homology classes on algebraic varieties
Izvestiya. Mathematics , Tome 1 (1967) no. 2, pp. 209-251

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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 $V$. 
@article{IM2_1967_1_2_a1,
     author = {B. G. Moishezon},
     title = {Algebraic homology classes on algebraic varieties},
     journal = {Izvestiya. Mathematics },
     pages = {209--251},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1967},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a1/}
}
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B. G. Moishezon. Algebraic homology classes on algebraic varieties. Izvestiya. Mathematics , Tome 1 (1967) no. 2, pp. 209-251. http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a1/