Displaying similar documents to “A Hartogs type extension theorem for generalized (N,k)-crosses with pluripolar singularities”

The jump of the Milnor number in the X 9 singularity class

Szymon Brzostowski, Tadeusz Krasiński (2014)

Open Mathematics

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The jump of the Milnor number of an isolated singularity f 0 is the minimal non-zero difference between the Milnor numbers of f 0 and one of its deformations (f s). We prove that for the singularities in the X 9 singularity class their jumps are equal to 2.

Extreme plurisubharmonic singularities

Alexander Rashkovskii (2012)

Annales Polonici Mathematici

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A plurisubharmonic singularity is extreme if it cannot be represented as the sum of non-homothetic singularities. A complete characterization of such singularities is given for the case of homogeneous singularities (in particular, those determined by generic holomorphic mappings) in terms of decomposability of certain convex sets in ℝⁿ. Another class of extreme singularities is presented by means of a notion of relative type.

A remark on the identity principle for analytic sets

Marek Jarnicki, Peter Pflug (2011)

Colloquium Mathematicae

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We present a version of the identity principle for analytic sets, which shows that the extension theorem for separately holomorphic functions with analytic singularities follows from the case of pluripolar singularities.