  Resorting to the characteristic polynomial of Lax matrix for the Dym-type
hierarchy, we define a trigonal curve, on which appropriate vector-valued
Baker-Akhiezer function and meromorphic function are introduced. Based on the
theory of trigonal curve and three kinds of Abelian differentials, we obtain
the explicit Riemann theta function representations of the meromorphic
function, from which we get the algebro-geometric constructions for the entire
Dym-type hierarchy
