Multi-Logarithmic Differential Forms on Complete Intersections

Alexandr G. Aleksandrov ; Avgust K. Tsikh

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 2, pp. 105-124

Résumé

We construct a complex $\Omega_S^\bullet(\log C)$ of sheaves of multi-logarithmic differential forms on a complex analytic manifold $S$ with respect to a reduced complete intersection $C\subset S$, and define the residue map as a natural morphism from this complex onto the Barlet complex $\omega_C^\bullet$ of regular meromorphic differential forms on $C$. 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.

Détail

Keywords: complete intersection, multi-logarithmic differential forms, regular meromorphic differential forms, Poincaré residue, logarithmic residue, Grothendieck duality, residue current.