Geodesic
On the homology groups of arrangements of complex planes of codimension two
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2009), pp. 33-39

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In the study of two-dimensional compact toric varieties, there naturally appears a set of coordinate planes of codimension two $Z=\cup_{1|i-j|$ in $\mathbb C^d$. Based on the Alexander–Pontryagin duality theory, we construct a cycle that is dual to the generator of the highest dimensional nontrivial homology group of the complement in $\mathbb C^d$ of the set of planes $Z$. We explicitly describe cycles that generate groups $H_{d+2}(\mathbb C^d\setminus Z)$ and $H_{d-3}(\overline Z)$, where $\overline Z=Z\cup\{\infty\}$.
Keywords: toric varieties
Mots-clés : plane arrangements. 
@article{IVM_2009_10_a3,
     author = {A. V. Kazanova and Yu. V. Eliyashev},
     title = {On the homology groups of arrangements of complex planes of codimension two},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {33--39},
     publisher = {mathdoc},
     number = {10},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_10_a3/}
}
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A. V. Kazanova; Yu. V. Eliyashev. On the homology groups of arrangements of complex planes of codimension two. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2009), pp. 33-39. http://geodesic.mathdoc.fr/item/IVM_2009_10_a3/