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

A. M. Nefedova

National Research University Higher School of Economics, Moscow, Russia

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.

Keywords: Riemann–Hilbert problem, elliptic curve, logarithmic connection.

Received: 11.08.2025
Revised: 30.09.2025

DOI: 10.4213/tmf11065

 English version: Theoretical and Mathematical Physics, 2026, 226:2, 177–188