Locally Stein domains over holomorphically convex manifolds

Vâjâitu, Viorel

J. Math. Kyoto Univ., Tome 48 (2008) no. 4, p. 133-148 / Harvested from Project Euclid

Résumé

Let $\pi : Y \longrightarrow X$ be a domain over a complex space $X$. Assume that $\pi$ is locally Stein. Then we show that $Y$ is Stein provided that $X$ is Stein and either there is an open set $W$ containing $X_{\mathrm{sing}}$ with $\pi^{-1}(W)$ Stein or $\pi$ is locally hyperconvex over any point in $X_{\mathrm{sing}}$. In the same vein we show that, if $X$ is $q$-complete and $X$ has isolated singularities, then $Y$ results $q$-complete.

Publié le : 2008-05-15
Classification: 32E05, 32Txx, 32C55, 32F10

@article{1250280978,
     author = {V\^aj\^aitu, Viorel},
     title = {Locally Stein domains over holomorphically convex manifolds},
     journal = {J. Math. Kyoto Univ.},
     volume = {48},
     number = {4},
     year = {2008},
     pages = { 133-148},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250280978}
}

Vâjâitu, Viorel. Locally Stein domains over holomorphically convex manifolds. J. Math. Kyoto Univ., Tome 48 (2008) no. 4, pp.  133-148. http://gdmltest.u-ga.fr/item/1250280978/