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<p>On a symplectic manifold <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3805_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\((M,\omega ),\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> a spacefilling brane structure is a closed 2-form <i>F</i> which determines a complex structure, with respect to which <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3805_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(F+i\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>F</mi> <mo>+</mo> <mi>i</mi> <mi>ω</mi> </mrow> </math></EquationSource> </InlineEquation> is holomorphic symplectic. For holomorphic symplectic compact Kähler 4-manifolds, we show that the moduli space of spacefilling branes is smooth, and determine its dimension. The proof relies on the local Torelli theorem for K3 surfaces and tori.</p>

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Moduli spaces of spacefilling branes in symplectic 4-manifolds

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Charlotte Kirchhoff-Lukat,
  • Marco Zambon

摘要

On a symplectic manifold \((M,\omega ),\) ( M , ω ) , a spacefilling brane structure is a closed 2-form F which determines a complex structure, with respect to which \(F+i\omega \) F + i ω is holomorphic symplectic. For holomorphic symplectic compact Kähler 4-manifolds, we show that the moduli space of spacefilling branes is smooth, and determine its dimension. The proof relies on the local Torelli theorem for K3 surfaces and tori.