Correlation functions and spectral curves in models of minimal gravity

We discuss correlators for models of minimal gravity and propose an algorithm for calculating invariant relations from formulas for residues that can be compared with the expansion coefficients for the partition function in the Liouville theory. For $(2,2K-1)$ models, we explicitly obtain a factor corresponding to conversion from the semiclassical hierarchy basis to the Liouville theory basis and also test a hypothesis about the pattern of the spectral curve using a direct calculation.