## Multi-Logarithmic Differential Forms on Complete Intersections

### Abstract

We construct a complex of sheaves of multi-logarithmic differential forms on a complex analytic manifold with respect to a reduced complete intersection; and define the residue map as a natural morphism from this complex onto the Barlet complex of regular meromorphic differential forms: It follows then that sections of the Barlet complex can be regarded as a generalization of the residue differential forms defined by Leray. Moreover, we show that the residue map can be described explicitly in terms of certain integration current

Topics: complete intersection, multi-logarithmic differential forms, regular meromorphic differential forms, Poincar'e residue, logarithmic residue, Grothendieck duality, residue current
Publisher: Сибирский федеральный университет. Siberian Federal University
Year: 2020
OAI identifier: oai:rour.neicon.ru:rour/265076