Geodesic
Cohomology of complexes of meromorphic forms and residues
Izvestiya. Mathematics, Tome 6 (1972) no. 6, pp. 1217-1250 
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/
@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},
     year = {1972},
     volume = {6},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_6_a2/}
}
TY  - JOUR
AU  - V. A. Krasnov
TI  - Cohomology of complexes of meromorphic forms and residues
JO  - Izvestiya. Mathematics
PY  - 1972
SP  - 1217
EP  - 1250
VL  - 6
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/IM2_1972_6_6_a2/
LA  - en
ID  - IM2_1972_6_6_a2
ER  - 
%0 Journal Article
%A V. A. Krasnov
%T Cohomology of complexes of meromorphic forms and residues
%J Izvestiya. Mathematics
%D 1972
%P 1217-1250
%V 6
%N 6
%U http://geodesic.mathdoc.fr/item/IM2_1972_6_6_a2/
%G en
%F IM2_1972_6_6_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Atiyah M. F., Hodge W. V., “Integrals of the second kind on a algebraic variety”, Ann. Math., 62 (1955), 56–91 | DOI | MR | Zbl

[2] Deligne P., Theorie de Hodge, preprint

[3] Griffiths P. A., “On the periods of certain rational integrals. I, II”, Ann. Math., 90:3 (1969), 460–541 | DOI | MR | Zbl

[4] Grothendieck A., “On the de Rham cohomology of algebraic varietes”, Publ. Math. IHES, 29 (1966), 95–103 | MR

[5] Leray J., “Le calcul différentiel et intégral sur une varieté analytique complexe (Probléme de Cauchy III)”, Bull. Soc. math. Fr., 87 (1959), 81–180 ; Differentsialnoe i integralnoe ischislenie na kompleksnom analiticheskom mnogoobrazii, IL, M., 1961 | MR | Zbl

[6] Bott R., “Homogeneous vector bundles”, Ann. Math.(2), 66 (1957), 203–248 | DOI | MR | Zbl