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arXiv · 1810.09115

Automorphism groups of almost homogeneous varieties

Michel Brion
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Abstract

Consider a smooth connected algebraic group $G$ acting on a normal projective variety $X$ with an open dense orbit. We show that Aut($X$) is a linear algebraic group if so is $G$; for an arbitrary $G$, the group of components of Aut($X$) is arithmetic. Along the way, we obtain a restrictive condition for $G$ to be the full automorphism group of some normal projective variety.

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Michel Brion. 2018-10-22. Automorphism groups of almost homogeneous varieties. https://arxiv.org/abs/1810.09115

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