On the weight filtration of the homology of algebraic varieties : the generalized Leray cycles
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 4, pp. 869-903.

Let Y be a normal crossing divisor in the smooth complex projective algebraic variety X and let U be a tubular neighbourhood of Y in X. Using geometrical properties of different intersections of the irreducible components of Y, and of the embedding YX, we provide the “normal forms” of a set of geometrical cycles which generate 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,) of Deligne’s mixed Hodge structure. The main technical part is to construct “the generalized Leray inverse image” of chains of the components of Y, giving rise to a chain situated in U.

Classification : 14C30, 14F25
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     title = {On the weight filtration of the homology of algebraic varieties : the generalized {Leray} cycles},
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Elzein, Fouad; Némethi, András. On the weight filtration of the homology of algebraic varieties : the generalized Leray cycles. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 4, pp. 869-903. http://www.numdam.org/item/ASNSP_2002_5_1_4_869_0/

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