Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normalit\'e projective des var\'et\'es magnifiques de rang 1   Let $L$ and $L'$ be two invertible sheaves over a projective variety $X$. We
suppose that $L$ and $L'$ are generated by their global section spaces
$\Gamma(L)$ and $\Gamma(L')$. We prove in this article that the morphism :
\[\Gamma(L) \otimes \Gamma(L') \to \Gamma(L \otimes L')\] is surjective, in the
case where $X$ is a rank one wonderful variety. In particular, the cone over a
rank one wonderful variety defined by a very ample invertible sheaf is always
normal. Soient $L$ et $L'$ deux faisceaux inversibles sur une vari\'et\'e
projective $X$. On suppose que $L$ et $L'$ sont engendr\'es par leurs espaces
de sections globales $\Gamma(L)$ et $\Gamma(L')$. On d\'emontre dans cet
article que le morphisme : \[\Gamma(L) \otimes \Gamma(L') \to \Gamma(L \otimes
L')\] est surjectif, dans le cas o\`u $X$ est une vari\'et\'e magnifique de
rang 1. En particulier, le c\^one au-dessus d'une vari\'et\'e magnifique $X$ de
rang 1 d\'efini par un faisceau inversible tr\`es ample est toujours normal.

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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn