This article is cited in 1 scientific paper (total in 1 paper)
The Index of Differential Forms on Complete Intersections
A. G. Aleksandrov
V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow
The article is devoted to the development of a homological approach to the problem of calculating the local topological index of holomorphic differential $1$-forms given on complex space. In the study of complete intersections our method is based on the construction of Lebelt and Cousin resolutions, as well as on the simplest properties of the generalized and usual Koszul complexes, regular meromorphic differential forms, and the residue map. In particular, we show that the index of a differential $1$-form with an isolated singularity is equal to the dimension of the local analytical algebra of a zero-dimensional germ which is determined by the ideal generated by the interior product of the form and all Hamiltonian vector fields of the complete intersection. Moreover, in the quasihomogeneous case, the index can be expressed explicitly in terms of values of classical symmetric functions.
We also discuss some other methods for computing the homological index of $1$-forms given on analytic spaces with singularities of various types.
index of differential forms, homological index, isolated complete intersection singularities, de Rham complex, Koszul complex, regular meromorphic forms
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Functional Analysis and Its Applications, 2015, 49:1, 1–14
A. G. Aleksandrov, “The Index of Differential Forms on Complete Intersections”, Funktsional. Anal. i Prilozhen., 49:1 (2015), 1–17; Funct. Anal. Appl., 49:1 (2015), 1–14
Citation in format AMSBIB
\paper The Index of Differential Forms on Complete Intersections
\jour Funktsional. Anal. i Prilozhen.
\jour Funct. Anal. Appl.
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This publication is cited in the following articles:
A. G. Aleksandrov, “Differential Forms on Quasihomogeneous Noncomplete Intersections”, Funct. Anal. Appl., 50:1 (2016), 1–16
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