Geodesic
On the cycles separating the system of~$m$ hypersurfaces in the neighbourhood of the point in~$\mathbb C^n$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 2, pp. 276-282

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It is known, that any $n$-cycle on a Stein manifold of dimension $n$, which topologically separates $n$ hypersurfaces, is homologous to the linear combination of the local cycles in the discrete intersection of the hypersurfaces. In this paper we consider the case when $m>n$. Particulary, we proof that in the local case, if $m=n+1$, such cycles is also related with discrete intersection of $n$-subsets of hiperfaces.
Keywords: separating cycle, local residue, local cycle. 
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     author = {Roman V. Ulvert},
     title = {On the cycles separating the system of~$m$ hypersurfaces in the neighbourhood of the point in~$\mathbb C^n$},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {276--282},
     publisher = {mathdoc},
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     number = {2},
     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/JSFU_2012_5_2_a14/}
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Roman V. Ulvert. On the cycles separating the system of~$m$ hypersurfaces in the neighbourhood of the point in~$\mathbb C^n$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 2, pp. 276-282. http://geodesic.mathdoc.fr/item/JSFU_2012_5_2_a14/