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Teorema de irreducibilidad para correspondencias algebraicas.

Eugenio Roanes (1980)

Revista Matemática Hispanoamericana

Sea T una correspondencia algebraica irreducible entre dos variedades proyectivas, V y V', sobre un cuerpo k algebraicamente cerrado y de característica cero. Sea W una subvariedad irreducible de V y W' = T{W} la transformada total de W en T. En [1] se estudia el problema de la conexión de W' y en [3] se estudia el problema de la irreducibilidad de la transformada total de W en correspondencias locales. La finalidad de este artículo es la de aprovechar los resultados de los dos trabajos citados,...

The Briançon-Skoda number of analytic irreducible planar curves

Jacob Sznajdman (2014)

Annales de l’institut Fourier

The Briançon-Skoda number of a ring R is defined as the smallest integer k, such that for any ideal I ⊂ R and l ≥ 1 , the integral closure of I k + l - 1 is contained in I l . We compute the Briançon-Skoda number of the local ring of any analytic irreducible planar curve in terms of its Puiseux characteristics. It turns out that this number is closely related to the Milnor number.

The Łojasiewicz numbers and plane curve singularities

Evelia García Barroso, Tadeusz Krasiński, Arkadiusz Płoski (2005)

Annales Polonici Mathematici

For every holomorphic function in two complex variables with an isolated critical point at the origin we consider the Łojasiewicz exponent ₀(f) defined to be the smallest θ > 0 such that | g r a d f ( z ) | ≥ c | z | θ near 0 ∈ ℂ² for some c > 0. We investigate the set of all numbers ₀(f) where f runs over all holomorphic functions with an isolated critical point at 0 ∈ ℂ².

The monodromy conjecture for zeta functions associated to ideals in dimension two

Lise Van Proeyen, Willem Veys (2010)

Annales de l’institut Fourier

The monodromy conjecture states that every pole of the topological (or related) zeta function induces an eigenvalue of monodromy. This conjecture has already been studied a lot. However in full generality it is proven only for zeta functions associated to polynomials in two variables.In this article we work with zeta functions associated to an ideal. First we work in arbitrary dimension and obtain a formula (like the one of A’Campo) to compute the “Verdier monodromy” eigenvalues associated to an...

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