The geometry of generalized Lamé equation, I

Zhijie Chen, Ting Jung Kuo, Chang Shou Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)89-120
Number of pages32
JournalJournal des Mathematiques Pures et Appliquees
Publication statusPublished - 2019 Jul


  • Degree of the addition map
  • Generalized Lamé equation
  • Spectral curve

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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