I'd like to get my hands on some simple examples of families of stable curves. Ideally these would come in the form of a projective curve $C$ over a 1 dimensional base $B$, say $B = \mathbb{A}^1$. The generic fiber would be smooth and the special fiber would be nodal.
For genus 0 there is the nice example of the closure in $\mathbb{P}^2_{\mathbb{A}^1}$ of Spec $k[x,y,t]/(xy - t)$ where $t$ is the coordinate on $\mathbb{A}^1$.
For genus 1 there is the closure in $\mathbb{P}^2_{\mathbb{A}^1}$ of Spec $k[x,y,t]/(y^2 = x(x-t)(x+1))$.
I know for genus $2$ you can't expect to have an example in $\mathbb{P}^2_{\mathbb{A}^1}$ but what about something in $\mathbb{P}^3_{\mathbb{A}^1}$?
Whenever $g = (d-1)(d-2)/2$ I would think you can get an example in $\mathbb{P}^2_{\mathbb{A}^1}$, is there anyway to control the number of nodes you get in the special fiber?