Grauert's line bundle convexity, reduction and Riemann domains

Vâjâitu, Viorel. "Grauert's line bundle convexity, reduction and Riemann domains." Czechoslovak Mathematical Journal 66.2 (2016): 493-509. <http://eudml.org/doc/280097>.

@article{Vâjâitu2016,
abstract = {We consider a convexity notion for complex spaces $X$ with respect to a holomorphic line bundle $L$ over $X$. This definition has been introduced by Grauert and, when $L$ is analytically trivial, we recover the standard holomorphic convexity. In this circle of ideas, we prove the counterpart of the classical Remmert’s reduction result for holomorphically convex spaces. In the same vein, we show that if $H^0(X,L)$ separates each point of $X$, then $X$ can be realized as a Riemann domain over the complex projective space $\mathbb \{P\}^n$, where $n$ is the complex dimension of $X$ and $L$ is the pull-back of $\{\mathcal \{O\}\}(1)$.},
author = {Vâjâitu, Viorel},
journal = {Czechoslovak Mathematical Journal},
keywords = {Grauert's line bundle convexity; Riemann domain; holomorphic reduction},
language = {eng},
number = {2},
pages = {493-509},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Grauert's line bundle convexity, reduction and Riemann domains},
url = {http://eudml.org/doc/280097},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Vâjâitu, Viorel
TI - Grauert's line bundle convexity, reduction and Riemann domains
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 493
EP - 509
AB - We consider a convexity notion for complex spaces $X$ with respect to a holomorphic line bundle $L$ over $X$. This definition has been introduced by Grauert and, when $L$ is analytically trivial, we recover the standard holomorphic convexity. In this circle of ideas, we prove the counterpart of the classical Remmert’s reduction result for holomorphically convex spaces. In the same vein, we show that if $H^0(X,L)$ separates each point of $X$, then $X$ can be realized as a Riemann domain over the complex projective space $\mathbb {P}^n$, where $n$ is the complex dimension of $X$ and $L$ is the pull-back of ${\mathcal {O}}(1)$.
LA - eng
KW - Grauert's line bundle convexity; Riemann domain; holomorphic reduction
UR - http://eudml.org/doc/280097
ER -