0100492108

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An open set satisfying a local intermediate cousin-I condition in a complex space

Japanese (日本語)

Kobe Journal of Mathematics

40

47-56

理学研究科数学専攻

2023

Let D be an open set in a pure n-dimensional complex space X, q an integer such that 1 ≤ q ≤ n and S(X) the set of singular points in X. In this paper, we prove the following two theorems: If D is exhausted by open sets {Dν} such that Hq(Dν ∩ U,O) → Hq(Dν ∩ U,M) is injective for every ν ∈ N and for every relatively compact Stein open set U, then D is locally q-complete with corners at every point x ∈ ∂D/ S(X). If D has a continuous boundary and Hq(D∩U,O)→ Hq(D ∩ U,M) is injective for every relatively compact Stein open set U, then D is locally q-complete with corners at every point x ∈ ∂D / S(X).

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