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arXiv · 2007.07882

Isolated torus invariants and automorphism groups of rigid varieties

Viktoria Borovik·Sergey Gaifullin
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Abstract

Perepechko and Zaidenberg conjectured that the neutral component of the automorphism group of a rigid affine variety is a torus. We prove this conjecture for toric varieties and varieties with a torus action of complexity one. We also obtain a criterion for an $m$-suspension over a rigid variety to be rigid (for every rigid variety and every regular function). Additionally, we study the automorphism group of $m$-suspensions satisfying this criterion.

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Viktoria Borovik, Sergey Gaifullin. 2020-07-15. Isolated torus invariants and automorphism groups of rigid varieties. https://arxiv.org/abs/2007.07882

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