<p>We obtain explicit formulae for the Donagi–Markman (Bryant–Griffiths, Yukawa) cubic for Hitchin systems of type <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13398_2025_1741_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$A_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13398_2025_1741_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$B_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>B</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13398_2025_1741_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$G_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>. This is achieved by evaluating the quadratic residues in the Balduzzi–Pantev formula, using a previous result of ours. For <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13398_2025_1741_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$G_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> we also recover earlier results of Hitchin.</p>

Donagi–Markman cubics for Hitchin systems of type $A_2$, $B_2$, $G_2$

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2025年5月29日

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Ugo Bruzzo,
Peter Dalakov

摘要

We obtain explicit formulae for the Donagi–Markman (Bryant–Griffiths, Yukawa) cubic for Hitchin systems of type $A_2$ $A_{2}$ , $B_2$ $B_{2}$ and $G_2$ $G_{2}$ . This is achieved by evaluating the quadratic residues in the Balduzzi–Pantev formula, using a previous result of ours. For $G_2$ $G_{2}$ we also recover earlier results of Hitchin.

Donagi–Markman cubics for Hitchin systems of type \(A_2\), \(B_2\), \(G_2\)

摘要