11 August 2017
14 July 2017
14 June 2017
We study effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line.
A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and the explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic.
We consider a generalization of Riemann–Hilbert problem on elliptic curves. For a given elliptic curve and irreducible representation of free group with two generators we construct explicitly a semistable vector bundle of degree zero obeying a logarithmic connection such that its monodromy over fundamental parallelogram is equivalent to given free group representation, monodromy along a−cycle is trivial and monodromy along b−cycle belong to certain orbit.
A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and an explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic.