2020/11/17 by Viktoriia Borovik, Borovik, Viktoriia, Sergey Gaifullin +3
Mathematics · #Advanced Algebra and Geometry #Finite Group Theory Research #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2011.08514
By a commutative action on a smooth quadric Qn in Pn+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 Q2 up to equivalence, for n = 1 there are two commutative actions on Q1 up to equivalence.