Reduction of divisors and Clebsch system

Abstract

In 2015 Magri and Skrypnyk found Abel's equations for the Clebsch system on a couple of genus three spectral curves of 2 × 2 and 3 × 3 Lax matrices. Because both spectral curves are twofold coverings of elliptic curves, separated variables form two reduced divisors on these elliptic curves, which completely define two classes of linearly equivalent divisors. We want to reconstruct these classes of equivalent divisors starting with poles of the corresponding Baker-Akhiezer functions and standard reduction of divisors on elliptic curves. In this note, we discuss reduction of divisors on a spectral curve of 3 × 3 Lax matrix having a natural generalization to gl * (n) case.