Geodesic
On computability of multiple integrals by means of a sum of local residues
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 996-1010

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We consider $n$-fold integrals of meromorphic differential $n$-forms on an $n$-dimensional complex manifold and study the problem of computability of such integrals by means of local (Grothendieck) residues of these forms. This problem is relevant in various fields of theoretical physics (in superstring theory for study of periods of Calabi–Yau manifolds, in particle physics for computation of anomalous magnetic moments of muons). The obtained theorems refine earlier results of A.K. Tsikh and A.P. Yuzhakov.
Keywords: local residue, local cycle, separating cycle. 
@article{SEMR_2018_15_a133,
     author = {R. V. Ulvert},
     title = {On computability of multiple integrals by means of a sum of local residues},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {996--1010},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a133/}
}
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R. V. Ulvert. On computability of multiple integrals by means of a sum of local residues. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 996-1010. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a133/