TOPOLOGY OF ALGEBRAIC VARIETIES

FOUAD ELZEIN ANDRÁS NÉMETHI

Abstract. Let Y be a normal crossing divisor in the smooth projective algebraic variety X (defined over ℂ) and let U be a tubular neighbourhood of Y in X. We construct homological cycles generating H_{∗}(A, B), where (A, B) is one of the following pairs (Y, ∅), (X, Y), (X, X − Y), (X − Y, ∅) and (∂U, ∅). The construction is compatible with the weights in H_{∗}(A, B, ℚ) of Deligne’s mixed Hodge structure.