Extension et division dans les variétés à croisements normaux

Autores: Abderrabi Maati, Emmanuel Mazzilli
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 45, Nº 2, 2001, págs. 343-369
Idioma: francés
DOI: 10.5565/publmat_45201_03
Títulos paralelos:
- Extensión y división en variedades con cruces normales
- Extension and division in normal crossing varieties
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Resumen
- Let D be a bounded strictly pseudoconvex domain with smooth boundary and f = (f1, ..., fp) (fi Î Hol(D)) a complete intersection with normal crossing. In this paper we study an extension problem in L8-norm for holomorphic functions defined on f-1(0) n D and a decomposition formula g = ?i=1p figi for holomorphic functions g Î I(f1, ..., fp)(D) in Lipschitz spaces. We stress that for the two problems the classical theorem cannot be applied because f-1(0) has singularities on the boundary ?D. This work is the first step to understand this type of problem in the general singular case.