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Lagrangian planes in hyperk\"ahler varieties of $K3^{[n]}$-type

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arxiv 2206.10288 v1 pith:7KWC5QPI submitted 2022-06-21 math.AG

Georg Oberdieck This is my paper · ORCID
classification math.AG
keywords classahlerhyperklagrangianlinetypeconjectureconjectured
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abstract

Jieao Song recently conjectured a formula for the class of a Lagrangian plane on a hyperk\"ahler 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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  1. O'Grady's tenfolds from stable bundles on hyper-K\"ahler fourfolds

    math.AG 2024-11 conditional novelty 7.0 of 10

    A moduli-space construction realizes the Laza-Saccà-Voisin compactification and yields infinitely many new families of O'Grady's ten-dimensional hyper-Kähler manifolds.

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