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Abstract <p> In this paper, which is a follow-up of the previous ones (arXiv: 2406.14414 [math.AG] and arXiv: 2511.05117 [math.AG]), we extend the explicit parametrization of torsion-free rank <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(1\)</EquationSource> </InlineEquation> sheaves on projective irreducible curves with vanishing cohomology groups obtained earlier to an analogous parametrization of torsion-free sheaves of arbitrary rank with vanishing cohomology groups on projective irreducible curves. As an illustration of our theorem we calculate an explicit example, namely, the parametrization of rank <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(2\)</EquationSource> </InlineEquation> sheaves on the Weierstrass cubic curve. </p>

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Normal Forms for Ordinary Differential Operators. III

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Junhu Guo,
  • Alexander B. Zheglov

摘要

Abstract

In this paper, which is a follow-up of the previous ones (arXiv: 2406.14414 [math.AG] and arXiv: 2511.05117 [math.AG]), we extend the explicit parametrization of torsion-free rank \(1\) sheaves on projective irreducible curves with vanishing cohomology groups obtained earlier to an analogous parametrization of torsion-free sheaves of arbitrary rank with vanishing cohomology groups on projective irreducible curves. As an illustration of our theorem we calculate an explicit example, namely, the parametrization of rank \(2\) sheaves on the Weierstrass cubic curve.