Definition 107.21.2. Let $f : X \to S$ be a family of curves. We say $f$ is a semistable family of curves if

1. $X \to S$ is a prestable family of curves, and

2. $X_ s$ has genus $\geq 1$ and does not have a rational tail for all $s \in S$.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).