Commutative actions on smooth projective quadrics

Equivariant completions of affine spaces

“…In [20] the authors obtained a generalization of the Hassett-Tschinkel correspondence for induced actions of commutative linear algebraic groups on non-degenerate quadrics with open orbit. In [20], Theorem 3, it was proved that, apart from the unique additive action from Theorem 2.25, there are only three cases: a G m -action on Q 1 , a G a × G m -action on Q 2 , and a G 2 m -action on Q 2 . At the same time, additive actions on degenerate quadrics are not unique.…”