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<p>In this paper, we consider a six parameter family of affine Segre surfaces embedded in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb C^6\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="double-struck">C</mi> <mn>6</mn> </msup> </math></EquationSource> </InlineEquation>. For generic values of the parameters, this family is associated to the <i>q</i>-difference sixth Painlevé equation. We show that different limiting forms of this family give Segre surfaces that are isomorphic as affine varieties to the monodromy manifolds of each Painlevé differential equation.</p>

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Segre Surfaces and Geometry of the Painlevé Equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年8月1日

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  • Nalini Joshi,
  • Marta Mazzocco,
  • Pieter Roffelsen

摘要

In this paper, we consider a six parameter family of affine Segre surfaces embedded in \(\mathbb C^6\) C 6 . For generic values of the parameters, this family is associated to the q-difference sixth Painlevé equation. We show that different limiting forms of this family give Segre surfaces that are isomorphic as affine varieties to the monodromy manifolds of each Painlevé differential equation.