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On Bochner-Martinelli residue currents and their annihilator ideals

Mattias Jonsson, Elizabeth Wulcan (2009)

Annales de l’institut Fourier

We study the residue current R f of Bochner-Martinelli type associated with a tuple f = ( f 1 , ⋯ , f m ) of holomorphic germs at 0 ∈ C n , whose common zero set equals the origin. Our main results are a geometric description of R f in terms of the Rees valuations associated with the ideal ( f ) generated by f and a characterization of when the annihilator ideal of R f equals ( f ) .

On the Briançon-Skoda theorem on a singular variety

Mats Andersson, Håkan Samuelsson, Jacob Sznajdman (2010)

Annales de l’institut Fourier

Let Z be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring 𝒪 Z ; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.

On the Cauchy problem in a class of entire functions in several variables

Eugeni Leinartas (1996)

Banach Center Publications

We study the integral representation of solutions to the Cauchy problem for a differential equation with constant coefficients. The Cauchy data and the right-hand of the equation are given by entire functions on a complex hyperplane of ℂ n + 1 . The Borel transformation of power series and residue theory are used as the main methods of investigation.

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