On the automorphism group of a toral variety

2022/11/29 by Shafarevich, Anton, Trushin, Anton
#Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14L30

paper · doi:10.48550/arxiv.2211.16584

Abstract

Let \mathbbK be an algebraically closed field of characteristic zero. An affine algebraic variety X over \mathbbK is toral if it is isomorphic to a closed subvariety of a torus (\mathbbK^*)^d. We study the group Aut(X) of regular automorpshims of a toral variety X. We prove that if T is a maximal torus in Aut(X), then X is a direct product Y× T, where Y is a toral variety with a trivial maximal torus in the automorphism group. We show that knowing Aut(Y), one can compute Aut(X). In the case when the rank of the group \mathbbK[Y]^*/\mathbbK^* is dim Y + 1, the group Aut(Y) can be described explicitly.

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