This article is cited in 3 scientific papers (total in 3 papers)
Multi-Logarithmic Differential Forms on Complete Intersections
Alexandr G. Aleksandrova, Avgust K. Tsikhb
a Institute of Control Sciences, Russian Academy of Sciences
b Institute of Mathematics, Siberian Federal University
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.
complete intersection, multi-logarithmic differential forms, regular meromorphic differential forms, Poincaré residue, logarithmic residue, Grothendieck duality, residue current.
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Received in revised form: 10.04.2008
Alexandr G. Aleksandrov, Avgust K. Tsikh, “Multi-Logarithmic Differential Forms on Complete Intersections”, J. Sib. Fed. Univ. Math. Phys., 1:2 (2008), 105–124
Citation in format AMSBIB
\by Alexandr~G.~Aleksandrov, Avgust~K.~Tsikh
\paper Multi-Logarithmic Differential Forms on Complete Intersections
\jour J. Sib. Fed. Univ. Math. Phys.
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