Geodesic
Grauert's line bundle convexity, reduction and Riemann domains
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 493-509 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\Bbb {P}^n$, where $n$ is the complex dimension of $X$ and $L$ is the pull-back of ${\mathcal O}(1)$.
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 $\Bbb {P}^n$, where $n$ is the complex dimension of $X$ and $L$ is the pull-back of ${\mathcal O}(1)$.
DOI : 10.1007/s10587-016-0271-0
Classification : 32E05, 32E99, 32F17
Keywords: Grauert's line bundle convexity; Riemann domain; holomorphic reduction 
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Vâjâitu, Viorel. Grauert's line bundle convexity, reduction and Riemann domains. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 493-509. doi: 10.1007/s10587-016-0271-0

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