Integrable systems related to elliptic branched coverings

TL;DR

This paper introduces new integrable systems linked to elliptic branched coverings, explores their connection with elliptic Schlesinger systems, provides explicit forms for two-fold coverings, and discusses a trigonometric degeneration.

Contribution

It constructs novel integrable systems related to elliptic branched coverings and details their relation to elliptic Schlesinger systems, including explicit examples and degenerations.

Findings

New integrable systems associated with elliptic branched coverings.

Explicit form of the integrable system for two-fold coverings.

A trigonometric degeneration of the constructed systems.

Abstract

The new integrable systems associated to the space of elliptic branched coverings are constructed. The relationship of these systems with elliptic Schlesinger's system is described. For the standard two-fold elliptic coverings the integrable system is written explicitly. A trigonometric degeneration of the construction is presented.