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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 4, Pages 1–17 (Mi faa3126)  

The Multiple Residue and the Weight Filtration on the Logarithmic de Rham Complex

A. G. Aleksandrov

Institute of Control Sciences, Russian Academy of Sciences, Moscow

Abstract: We study the multiple residue of logarithmic differential forms with poles along a reducible divisor and compute the kernel and the image of the multiple residue map. As an application we describe the weight filtration on the logarithmic de Rham complex for divisors whose irreducible components are given locally by a regular sequence of holomorphic functions. In particular, this allows us to compute the mixed Hodge structure on the cohomology of the complement of divisors of certain types without the use of theorems on resolution of singularities and the standard reduction to the case of normal crossings.

Keywords: multiple residue, logarithmic differential forms, logarithmic de Rham complex, regular meromorphic forms, weight filtration

DOI: https://doi.org/10.4213/faa3126

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English version:
Functional Analysis and Its Applications, 2013, 47:4, 247–260

Bibliographic databases:

UDC: 515.17
Received: 28.12.2011

Citation: A. G. Aleksandrov, “The Multiple Residue and the Weight Filtration on the Logarithmic de Rham Complex”, Funktsional. Anal. i Prilozhen., 47:4 (2013), 1–17; Funct. Anal. Appl., 47:4 (2013), 247–260

Citation in format AMSBIB
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