Geodesic
Cohomology of complexes of meromorphic forms and residues
Izvestiya. Mathematics , Tome 6 (1972) no. 6, pp. 1217-1250

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We study the cohomology of complexes of meromorphic forms on a Kähler manifold whose poles lie on a fixed submanifold. We study the connection between the order of the pole of such forms and the type of their residue class depending on a infinitesimal neighborhood of the submanifold. 
@article{IM2_1972_6_6_a2,
     author = {V. A. Krasnov},
     title = {Cohomology of complexes of meromorphic forms and residues},
     journal = {Izvestiya. Mathematics },
     pages = {1217--1250},
     publisher = {mathdoc},
     volume = {6},
     number = {6},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_6_a2/}
}
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V. A. Krasnov. Cohomology of complexes of meromorphic forms and residues. Izvestiya. Mathematics , Tome 6 (1972) no. 6, pp. 1217-1250. http://geodesic.mathdoc.fr/item/IM2_1972_6_6_a2/