On polar invariants of hypersurface singularities
Alejandro Melle-Hernández (2000)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Alejandro Melle-Hernández (2000)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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.
János Kollár (1998)
Collectanea Mathematica
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The aim of this series of papers is to develop the theory of minimal models for real algebraic threefolds. The ultimate aim is to understand the topology of the set of real points of real algebraic threefolds. We pay special attention to 3–folds which are birational to projective space and, more generally, to 3–folds of Kodaira dimension minus infinity.present work contains the beginning steps of this program. First we classify 3–dimensional terminal singularities over any field of characteristic...
Clément Caubel, Mihai Tibăr (2003)
Banach Center Publications
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We survey some recent results concerning the behavior of the contact structure defined on the boundary of a complex isolated hypersurface singularity or on the boundary at infinity of a complex polynomial.
Alain Joets (2008)
Banach Center Publications
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When drawing regular surfaces, one creates a concrete and visual example of a projection between two spaces of dimension 2. The singularities of the projection define the apparent contour of the surface. As a result there are two types of generic singularities: fold and cusp (Whitney singularities). The case of singular surfaces is much more complex. A priori, it is expected that new singularities may appear, resulting from the "interaction" between the singularities of the surface and...
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.
Buchner, Klaus (1997)
General Mathematics
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Eric Dago Akéké (2008)
Annales de la faculté des sciences de Toulouse Mathématiques
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The purpose of this article is to show that are satisfied for complex analytic families of normal surface singularities for which the are . According to J. Briançon and J. P. Speder the constancy of the topological type of a family of surface singularities does not imply Whitney conditions in general. We will see here that for a family of these two equisingularity conditions are equivalent.
G.M. Greuel, H. Kröning (1990)
Mathematische Zeitschrift
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Guangfeng Jiang, Dirk Siersma (1999)
Annales de l'institut Fourier
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Lines on hypersurfaces with isolated singularities are classified. New normal forms of simple singularities with respect to lines are obtained. Several invariants are introduced.
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.