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In this paper we study certain degenerations of the mirror curves, associatedwith Calabi-Yau threefolds $X_{N,M}$, and the effect of these degenerations onthe topological string partition function of $X_{N,M}$. We show that when themirror curve degenerates and become the union of the lower genus curves thecorresponding partition function factorizes into pieces corresponding to thecomponents of the degenerate mirror curve. Moreoever we show that usingdegeneration of a generalised mirror curve it is possible to obtain thepartition function corresponding to $X_{N,M-1}$ from $X_{N,M}$.

Degeneration of Topological String partition functions and Mirror curves of the Calabi-Yau threefolds $X_{N,M}$