2020
DOI: 10.48550/arxiv.2011.08514
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Commutative actions on smooth projective quadrics

Abstract: By a commutative action on a smooth quadric Qn in P n+1 we mean an effective action of a commutative connected algebraic group on Qn with an open orbit. We show that for n ≥ 3 all commutative actions on Qn are additive actions described by Sharoiko in 2009. So there is a unique commutative action on Qn up to equivalence. For n = 2 there are three commutative actions on Q 2 up to equivalence, for n = 1 there are two commutative actions on Q 1 up to equivalence.

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