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<p>Jieao Song recently conjectured a formula for the class of a Lagrangian plane on a hyperkähler variety of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3755_Article_IEq1.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(K3^{[n]}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <msup> <mn>3</mn> <mrow> <mo stretchy="false">[</mo> <mi>n</mi> <mo stretchy="false">]</mo> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>-type in terms of the class of a line on it. We give a proof of this conjecture if the line class is primitive.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月7日

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  • Georg Oberdieck

摘要

Jieao Song recently conjectured a formula for the class of a Lagrangian plane on a hyperkähler variety of \(K3^{[n]}\) K 3 [ 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.