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We give a geometric description of the pair $(V,p)$, where $V$ is an affinealgebraic variety over a non-trivially valued algebraically closed field $K$with valuation ring $\mathcal{O}_K$ and $p$ is a Zariski dense genericallystable type concentrated on $V$, by defining a fully faithful functor to thecategory of schemes over $\mathcal{O}_K$ with residual dominant morphisms over$\mathcal{O}_K$.  We also study a maximum modulus principle on schemes over $\mathcal{O}_K$ andshow that the schemes obtained by this functor enjoy it.

On Stably Pointed Varieties and Generically Stable Groups in ACVF