Definition 107.20.1. Let $f : X \to S$ be a family of curves. We say $f$ is a *prestable family of curves* if

$f$ is at-worst-nodal of relative dimension $1$, and

$f_*\mathcal{O}_ X = \mathcal{O}_ S$ and this holds after any base change

^{1}.

Definition 107.20.1. Let $f : X \to S$ be a family of curves. We say $f$ is a *prestable family of curves* if

$f$ is at-worst-nodal of relative dimension $1$, and

$f_*\mathcal{O}_ X = \mathcal{O}_ S$ and this holds after any base change

^{1}.

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