Lieu des points exceptionnels et cône tangent multidirectionnel d'un courant positif fermé
✍ Scribed by Mongi Blel
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- French
- Weight
- 141 KB
- Volume
- 124
- Category
- Article
- ISSN
- 0007-4497
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✦ Synopsis
Locus of exceptional points and the multidirectional tangent cone of a closed positive current.
Let Ω be an open set in C n , with n 2 and let (X k ) k be a sequence of analytic sets of dimension p n -2 in Ω. We prove that there exists a positive (1, 1)-current T on Ω such that the tangent cone of T does not exist at any point of k X k . More precisely we prove that for every open set ω ⊂ Ω and for every analytic set of dimension p n -2 in Ω, there exists a closed positive current T of bidegree (1, 1) on Ω such that the tangent cone of T does not exist on X ∩ ω, moreover we prove that for every closed positive current Θ of bidegree (1, 1), the tangent cone of the current T + Θ does not exist at any point of X ∩ ω. In the last paragraph, we study the directional and the multidirectional tangent cone associated to a closed positive current.