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arXiv · 1912.06985

Some automorphism groups are linear algebraic

Michel Brion
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Abstract

Consider a normal projective variety $X$, a linear algebraic subgroup $G$ of Aut($X$), and the field $K$ of $G$-invariant rational functions on $X$. We show that the subgroup of Aut($X$) that fixes $K$ pointwise is linear algebraic. If $K$ has transcendence degree $1$ over $k$, then Aut($X$) is an algebraic group.

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Michel Brion. 2019-12-15. Some automorphism groups are linear algebraic. https://arxiv.org/abs/1912.06985

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