2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63175A new approach to the finite-gap property for the Heun equation is constructed. The relationship between the finite-dimensional invariant space and the spectral curve is clarified. The monodromies are calculated and are expressed as hyperelliptic integrals. Applications to the spectral problem for the $BC_1$ Inozemtsev model are obtained.24 pagesClassical Analysis and ODEsMathematical PhysicsQuantum AlgebraSpectral TheoryExactly Solvable and Integrable Systems33E15; 34B30; 14H70text