Study equations in Lax form and understand how they give rise to a spectral curve and a line bundle on it.

References:

• Mumford, D. "Tata Lectures on Theta, vol II", Progress in Math. 43, Birkhauser 1984
• Beauville, A. "Jacobiennes des courbes spectrales et systemes hamiltoniens completement integrables", Acta Math. 164, '90