E. M. Chirka (2003)
Annales Polonici Mathematici
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It is proved that any subharmonic function in a domain Ω ⊂ ℂⁿ which is plurisubharmonic outside of a real hypersurface of class C¹ is indeed plurisubharmonic in Ω.
John Scherk (1980)
Inventiones mathematicae
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Tari, Farid (1992)
Experimental Mathematics
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G.M. Greuel, H. Kröning (1990)
Mathematische Zeitschrift
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Gert-Martin Greuel (1986)
Manuscripta mathematica
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Buchner, Klaus (1997)
General Mathematics
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Siersma, Dirk, Smeltnik, Job (2000)
Georgian Mathematical Journal
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Stevens, Jan (1995)
Experimental Mathematics
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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.
Max Benson, Stephen S.-T. Yau (1990)
Mathematische Annalen
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Kurt Behnke, Constantin Kahn, Oswald Riemenschneider (1988)
Banach Center Publications
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Marko Roczeń (1988)
Banach Center Publications
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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.