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

preprint2022arXivOpen access

Jieao Song recently conjectured a formula for the class of a Lagrangian plane on a hyperkähler variety of $K3^{[n]}$ -type in terms of the class of a line on it. We give a proof of this conjecture if the line class is primitive.

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

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

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