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Let $R$ be a DVR, and $k$ residue field of $R$. We suppose that $X_{0}$ is a stable curve over Spec$k$.

Dose there exist a stable model $X$ over $R$ such that the special fiber isomorphic to $X_{0}$ ?

If we assume $R=C[[t]]$, where C is complex number field, how to find a deformation which make the generic fiber is smooth?

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Let $R$ be a DVR, and $k$ residue field of $R$. We suppose that $X_{0}$ is a stable curve over Spec$k$.

Dose there is exist a stable model $X$ over $R$ such that the special fiber isomorphic to $X_{0}$ ?

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# deformation of stable curve

Let $R$ be a DVR, and $k$ residue field of $R$. We suppose that $X_{0}$ is a stable curve over Spec$k$.

Dose there is a stable model $X$ over $R$ such that the special fiber isomorphic to $X_{0}$ ?