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Analyticité des conditions de Whitney strictes

Jean-Paul Speder (1973)

Annales de l'institut Fourier

Soient X un espace analytique complexe réduit de dimension pure et Y un sous-espace lisse de X de dimension pure tel que dimension Y < dimension X .L’ensemble des points de Y en lesquels les conditions de Whitney strictes ne sont pas satisfaites par ( X , Y ) est un sous-espace analytique propre de Y .

Approximation of sets defined by polynomials with holomorphic coefficients

Marcin Bilski (2012)

Annales Polonici Mathematici

Let X be an analytic set defined by polynomials whose coefficients a , . . . , a s are holomorphic functions. We formulate conditions on sequences a 1 , ν , . . . , a s , ν of holomorphic functions converging locally uniformly to a , . . . , a s , respectively, such that the sequence X ν of sets obtained by replacing a j ’s by a j , ν ’s in the polynomials converges to X.

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