Displaying similar documents to “Remarks on the generalized index of an analytic improper intersection”

On the index of contact

M. Montserrat Alonso Ferrero (2004)

Annales Polonici Mathematici

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We use the construction of the intersection product of two algebraic cones to prove that the multiplicity of contact of the cones at the vertex is equal to the product of their degrees. We give an example to show that in order to calculate the index of contact it is not sufficient to perform the analytic intersection algorithm with hyperplanes.

Relative tangent cone of analytic sets

Danuta Ciesielska (2012)

Annales Polonici Mathematici

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We give a characterization of the relative tangent cone of an analytic curve and an analytic set with an improper isolated intersection. Moreover, we present an effective computation of the intersection multiplicity of a curve and a set with s-metrization.

Intersection theory and separation exponent in complex analytic geometry

Ewa Cygan (1998)

Annales Polonici Mathematici

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We consider the intersection multiplicity of analytic sets in the general situation. We prove that it is a regular separation exponent for complex analytic sets and so it estimates the Łojasiewicz exponent. We also give some geometric properties of proper projections of analytic sets.

Stable families of analytic sets

Pandelis Dodos (2003)

Colloquium Mathematicae

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We give a different proof of the well-known fact that any uncountable family of analytic subsets of a Polish space with the point-finite intersection property must contain a subfamily whose union is not analytic. Our approach is based on the Kunen-Martin theorem.

On real algebraic links in S 3

R. Benedetti, M. Shiota (1998)

Bollettino dell'Unione Matematica Italiana

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Viene presentata una costruzione che, dato un arbitrario nodo L ⊆ S 3 , produce allo stesso tempo: 1) un'applicazione polinomiale f : R 4 , 0 → R 2 , 0 con singolarità (debolmente) isolata in 0 e L come tipo di nodo della singolarità; 2) una risoluzione delle singolarità di f nel senso di Hironaka. Specializzando la costruzione ai nodi fibrati otteniamo una versione debole (a meno di scoppiementi e nella categoria analitica reale) di un reciproco per il teorema di fibrazione di Milnor.