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 $Y\subset X$, we provide the “normal forms” of a set of geometrical cycles which generate ${H}_{*}\left(A,B\right)$, where $\left(A,B\right)$ is one of the following pairs $\left(Y,\varnothing \right)$, $\left(X,Y\right)$, $\left(X,X-Y\right)$, $\left(X-Y,\varnothing \right)$ and $\left(\partial U,\varnothing \right)$. The construction is compatible with the weights in ${H}_{*}\left(A,B,ℚ\right)$ 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 $\partial U$.

Classification : 14C30,  14F25
@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 = {http://www.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://www.numdam.org/item/ASNSP_2002_5_1_4_869_0/

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