Under Kirwan surjectivity, the period map from algebraic asymptotic hyperkähler structures on a hyperkähler quotient to a period chamber is a bijection.
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A Torelli-type theorem for hyperk\"{a}hler quotients
Under Kirwan surjectivity, the period map from algebraic asymptotic hyperkähler structures on a hyperkähler quotient to a period chamber is a bijection.