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<p>The Frobenius manifold structure on the space of rational functions with multiple simple poles is constructed. In particular, the dependence of the Saito-flat coordinates on the flat coordinates of the intersection form is studied. While some of the individual flat coordinates are complicated rational functions, they appear in the prepotential in certain combinations known as diagonal invariants, which turn out to be polynomial. Two classes are studied in more detail. These are generalisations of the Coxeter and extended-affine-Weyl orbit spaces for the group <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(W=W(\mathscr {A}_\ell )\,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mo>=</mo> <mi>W</mi> <mo stretchy="false">(</mo> <msub> <mi mathvariant="script">A</mi> <mi>ℓ</mi> </msub> <mo stretchy="false">)</mo> <mspace width="0.166667em" /> </mrow> </math></EquationSource> </InlineEquation>. An invariant theory is also developed.</p>

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Diagonal invariants and genus-zero Hurwitz Frobenius manifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月7日

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  • Alessandro Proserpio,
  • Ian A. B. Strachan

摘要

The Frobenius manifold structure on the space of rational functions with multiple simple poles is constructed. In particular, the dependence of the Saito-flat coordinates on the flat coordinates of the intersection form is studied. While some of the individual flat coordinates are complicated rational functions, they appear in the prepotential in certain combinations known as diagonal invariants, which turn out to be polynomial. Two classes are studied in more detail. These are generalisations of the Coxeter and extended-affine-Weyl orbit spaces for the group \(W=W(\mathscr {A}_\ell )\,\) W = W ( A ℓ ) . An invariant theory is also developed.