Algebraic-geometry approach to construction of semi-Hamiltonian systems of hydrodynamic type

In this paper, a class of semi-Hamiltonian diagonal systems of hydrodynamic type is constructed using algebraic-geometric methods. For such systems, hydrodynamic integrals and hydrodynamic symmetries are constructed from algebraic-geometric data. Besides, it is described what algebraic-geometric data distinguish in this class Hamiltonian diagonal systems with Hamiltonian structures defined by flat metrics (local Dubrovin–Novikov brackets) and metrics of constant curvature (nonlocal Mokhov–Ferapontov brackets).