ALGEBRAIC HOMOLOGY CLASSES ON ALGEBRAIC VARIETIES

Abstract

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.