The geometry of generalized Lam? equation, I
Journal
Journal des Mathematiques Pures et Appliquees
Journal Volume
127
Pages
89-120
Date Issued
2019
Author(s)
Abstract
In this paper, we prove that the spectral curve Γn of the generalized Lamé equation with the Treibich–Verdier potential [Fourmula presented] can be embedded into the symmetric space SymNEτ of the N-th copy of the torus Eτ, where N=∑nk. This embedding induces an addition map σn(⋅|τ) from Γn onto Eτ. The main result is to prove that the degree of σn(⋅|τ) is equal to ∑k=0 3nk(nk+1)/2. This is the first step toward constructing the pre-modular form associated with this generalized Lamé equation.
In this paper, we prove that the spectral curve Γn of the generalized Lamé equation with the Treibich–Verdier potential [Fourmula presented] can be embedded into the symmetric space SymNEτ of the N-th copy of the torus Eτ, where N=∑nk. This embedding induces an addition map σn(⋅|τ) from Γn onto Eτ. The main result is to prove that the degree of σn(⋅|τ) is equal to ∑k=0 3nk(nk+1)/2. This is the first step toward constructing the pre-modular form associated with this generalized Lamé equation.
Type
journal article