There exist a normal affine variety $B$ over a perfect field $k$, a codimension one point $b\in B^{(1)}$, a projective regular integral scheme $\mathscr{X}_{B}$ over $B$, and line bundles $\mathscr{L}_{B}$ and $\mathcal{A}_{B}$ over $\mathscr{X}_{B}$ such that there exist

1. (i)

   a flat morphism $h\colon\Spec K^{\circ}\to\Spec\mathcal{O}_{B,b}\to B$,

2. (ii)

   an isomorphism $\mathscr{X}_{B}\otimes_{B}\Spec K^{\circ}\stackrel{{\scriptstyle\sim}}{{\to}}\mathscr{X}$,

3. (iii)

   an isomorphism $h^{*}\mathscr{L}_{B}\stackrel{{\scriptstyle\sim}}{{\to}}\mathscr{L}$ over the isomorphism in (ii),

4. (iv)

   and an isomorphism $\mathcal{A}_{B}|_{\mathscr{X}_{B,\eta}}\stackrel{{\scriptstyle\sim}}{{\to}}\mathscr{L}_{B}|_{\mathscr{X}_{B,\eta}}$ where $\eta$ is the generic point of $B$ and the line bundle $\mathcal{A}_{B}$ on $\mathscr{X}_{B}$ is ample.

Usually we read all the isomorphisms above as identifications.