Let be a normal crossing divisor in the smooth complex projective algebraic variety and let be a tubular neighbourhood of in . Using geometrical properties of different intersections of the irreducible components of , and of the embedding , we provide the “normal forms” of a set of geometrical cycles which generate , where is one of the following pairs , , , and . The construction is compatible with the weights in of Deligne’s mixed Hodge structure. The main technical part is to construct “the generalized Leray inverse image” of chains of the components of , giving rise to a chain situated in .
@article{ASNSP_2002_5_1_4_869_0, author = {Elzein, Fouad and N\'emethi, Andr\'as}, title = {On the weight filtration of the homology of algebraic varieties : the generalized Leray cycles}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {869--903}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 1}, number = {4}, year = {2002}, zbl = {1098.14006}, mrnumber = {1991006}, language = {en}, url = {archive.numdam.org/item/ASNSP_2002_5_1_4_869_0/} }
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://archive.numdam.org/item/ASNSP_2002_5_1_4_869_0/
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