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Stein open subsets with analytic complements in compact complex spaces

Jing Zhang (2015)

Annales Polonici Mathematici

Let Y be an open subset of a reduced compact complex space X such that X - Y is the support of an effective divisor D. If X is a surface and D is an effective Weil divisor, we give sufficient conditions so that Y is Stein. If X is of pure dimension d ≥ 1 and X - Y is the support of an effective Cartier divisor D, we show that Y is Stein if Y contains no compact curves, H i ( Y , Y ) = 0 for all i > 0, and for every point x₀ ∈ X-Y there is an n ∈ ℕ such that Φ | n D | - 1 ( Φ | n D | ( x ₀ ) ) ∩ Y is empty or has dimension 0, where Φ | n D | is the map from...

Stratified Whitney jets and tempered ultradistributions on the subanalytic site

N. Honda, G. Morando (2011)

Bulletin de la Société Mathématique de France

In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold X . Then, we define stratified ultradistributions of Beurling and Roumieu type on X . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if X is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to X . Second, the tempered-stratified...

Sulle classi di Dolbeault di tipo ( 0 , n - 1 ) con singolarità in un insieme discreto

Paolo Zappa (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This paper shows how some techniques used for the meromorphic functions of one variable can be used for the explicit construction of a solution to the Mittag-Leffler problem for Dolbeault classes of tipe ( 0 , n - 1 ) with singularities in a discrete set of 𝐂 𝐧 and T n (a n -dimensional complex torus). A generalisation is given for the Weierstrass ζ and the Legendre relations.

Sur la transformation d’Abel-Radon des courants localement résiduels

Bruno Fabre (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

After recalling the definitions of the Abel-Radon transformation of currents and of locally residual currents, we show that the Abel-Radon transform ℛ ( α ) of a locally residual current α remains locally residual. Then a theorem of P. Griffiths, G. Henkin and M. Passare (cf. [7], [9] and [10]) can be formulated as follows  :Let U be a domain of the grassmannian variety G ( p , N ) of complex p -planes in N , U * : = ∪ t ∈ U H t be the corresponding linearly p -concave domain of N , and α be a locally residual current of bidegree ( N , p ) ....

Currently displaying 601 – 620 of 747