Compact sets with vanishing cohomology in Stein spaces and domains of holomorphy
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 3, p. 665-685

Let X be a Stein space. We study compact subsets K of X that are structurally acyclic, i.e., H i (K,𝒪 X )=0, for all i1. We show i) that such compact sets are natural in the sense that the canonical map from K into K ˜, the spectrum of the complex algebra Γ(K,𝒪 X ), is bijective, and ii) that the set of interior points of K is a domain of holomorphy in X. Motivated by this we give an extensive account of examples of domains of holomorphy in non-normal Stein spaces and prove several properties, like hereditarity via the normalization map. Finally, a straightforward criterion of non-acyclicity is given in terms of general Hartogs figures.

Published online : 2019-02-21
Classification:  32D05,  32C35,  32E10,  32C15
@article{ASNSP_2013_5_12_3_665_0,
     author = {V\^aj\^aitu, Viorel},
     title = {Compact sets with vanishing cohomology in Stein spaces and domains of holomorphy},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 12},
     number = {3},
     year = {2013},
     pages = {665-685},
     zbl = {1278.32010},
     mrnumber = {3137459},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2013_5_12_3_665_0}
}
Vâjâitu, Viorel. Compact sets with vanishing cohomology in Stein spaces and domains of holomorphy. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 3, pp. 665-685. http://www.numdam.org/item/ASNSP_2013_5_12_3_665_0/

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