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<p>Let <i>X</i> be a double EPW sextic, and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3751_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(\iota \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ι</mi> </math></EquationSource> </InlineEquation> its anti-symplectic involution. We relate the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3751_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(\iota \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ι</mi> </math></EquationSource> </InlineEquation>-anti-invariant part of the Chow group of zero-cycles of <i>X</i> with Voisin’s rational orbit filtration. For a general double EPW sextic <i>X</i>, we also relate the anti-invariant part of the Chow motive of <i>X</i> with the motive of a Gushel–Mukai fourfold. As an application of the first result, we obtain a similar result for certain Fano varieties of lines in cubics with infinite-order birational automorphisms.</p>

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Double EPW sextics and the Voisin filtration on zero-cycles

  • 期刊论文

  • 发表日期：

    2025年4月25日

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  • Michele Bolognesi,
  • Robert Laterveer

摘要

Let X be a double EPW sextic, and \(\iota \) ι its anti-symplectic involution. We relate the \(\iota \) ι -anti-invariant part of the Chow group of zero-cycles of X with Voisin’s rational orbit filtration. For a general double EPW sextic X, we also relate the anti-invariant part of the Chow motive of X with the motive of a Gushel–Mukai fourfold. As an application of the first result, we obtain a similar result for certain Fano varieties of lines in cubics with infinite-order birational automorphisms.