Limités d'espaces tangents

Generic sections of essentially isolated determinantal singularities

“…c) The hyperplanes H and H contain planes Q = P ∩ H and Q = P ∩ H given in Proposition 6.1. Then X ∩ Q and X ∩ Q are determinantal curves and by Proposition 6.1, we have that: (9) µ(X ∩ Q) = µ(X ∩ Q ).…”

“…The minimality of the Milnor number of generic sections of hypersurfaces with isolated singularities was studied by B. Teissier [17] and J.-P. Henry and Lê D. T. [9]. T. Gaffney [5] proved the result for ICIS and J. Snoussi considered the case of normal surfaces in C N .…”

Exceptional rays and bilipschitz geometry of real surface singularities

“…In [9], we extended work of Whitney [12], Lê [7], Teissier [8], and others [6] on limits of tangent spaces in the complex analytic setting to the case of real surfaces in R 3 . In recent years, there has been much progress on bilipschitz geometry for complex analytic surfaces (see, for example, [3], [4]), and it is again natural to ask whether, and how, results in the complex analytic case carry over to the reals.…”

Invariantes de variedades determinantais

“…Os primeiros resultados sobre minimalidade do número de Milnor de uma seção genérica foram obtidos por J.-P. G. Henry e D. T. Lê para hipersuperficies em C N em 1975, [25]. Esses resultados foram estendidos ao caso de interseções completas por Terence Gaffney, em [21].…”

“…[25] Um hiperplano H ⊂ C N não é limite de hiperplanos tangentes em X se e somente se µ(X ∩ H) é mínimo.…”