Singular holomorphic functions for which all fibre-integrals are smooth

Barlet, D.; Maire, H.

Barlet, D. ; Maire, H.

Annales Polonici Mathematici, Tome 75 (2000), p. 65-77 / Harvested from The Polish Digital Mathematics Library

Résumé

For a germ (X,0) of normal complex space of dimension n + 1 with an isolated singularity at 0 and a germ f: (X,0) → (ℂ,0) of holomorphic function with df(x) ≤ 0 for x ≤ 0, the fibre-integrals $s \mapsto \int_{f = s} ϱ ω^{'} ⋀ \bar{ω^{''}}, ϱ \in C_{c}^{\infty} (X), ω^{'}, ω^{''} \in Ω_{X}^{n}$ , are $C^{\infty}$ on ℂ* and have an asymptotic expansion at 0. Even when f is singular, it may happen that all these fibre-integrals are $C^{\infty}$ . We study such maps and build a family of examples where also fibre-integrals for $ω^{'}, ω^{''} \in ⍹_{X}$ , the Grothendieck sheaf, are $C^{\infty}$ .

Publié le : 2000-01-01

Zbl 0961.32012

EUDML-ID : urn:eudml:doc:208377

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     author = {Barlet, D. and Maire, H.},
     title = {Singular holomorphic functions for which all fibre-integrals are smooth},
     journal = {Annales Polonici Mathematici},
     volume = {75},
     year = {2000},
     pages = {65-77},
     zbl = {0961.32012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv74z1p65bwm}
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Barlet, D.; Maire, H. Singular holomorphic functions for which all fibre-integrals are smooth. Annales Polonici Mathematici, Tome 75 (2000) pp. 65-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv74z1p65bwm/

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