The density problem for infinite dimensional group actions

S. Klimek; W. Kondracki; W. Oledzki; P. Sadowski

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We consider a smooth projective variety $X$ on which a simple algebraic group $G$ acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of $G$ with the induced action of $G$ on the normal bundle of a closed orbit of the action. We get effective results in case $G = S L (n)$ and $dim X \leq 2 n - 2$ .