Lagrangian planes in hyperkähler varieties of $$K3^{[n]}$$-type

Abstract Jieao Song recently conjectured a formula for the class of a Lagrangian plane on a hyperkähler variety of $$K3^{[n]}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>K</mml:mi> <mml:msup> <mml:mn>3</mml:mn> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>n</mml:mi> <mml:mo>]</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> -type in terms of the class of a line on it. We give a proof of this conjecture if the line class is primitive.