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Abstract <p> We obtain an explicit solution of the Riemann–Hilbert problem on an elliptic curve for the two-dimensional commutative monodromy representations. By an arbitrary set of points together with a representation of the fundamental group of the curve punctured at these points, we construct a semistable holomorphic vector bundle of degree zero with a logarithmic connection possessing the required singularities and monodromy. </p>

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Two-dimensional Riemann–Hilbert problem for commutative monodromy on an elliptic curve

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • A. M. Nefedova

摘要

Abstract

We obtain an explicit solution of the Riemann–Hilbert problem on an elliptic curve for the two-dimensional commutative monodromy representations. By an arbitrary set of points together with a representation of the fundamental group of the curve punctured at these points, we construct a semistable holomorphic vector bundle of degree zero with a logarithmic connection possessing the required singularities and monodromy.