Let $X$ be a stable curve consisting of two components meeting at three points. Let $M$ be its versal deformation space. The locus in $M$ parametrizing singular curves is a divisor with three components $D_1, D_2, D_3$, each corresponding to a node on $X$. The question is, which curve does a general point on $D_1\cap D_2$ correspond to? More precisely, does it correspond to an irreducible nodal curve, or a curve with two components meeting at two points?
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A general point on $D_1 \cap D_2$ is given by smoothing the third node, which produces an irreducible curve with two nodes. 

