Let $f:X \to \mbox{Spec}(R)$ be a flat, projective morphism with $R$ a discrete valuation ring and the special and generic fibers of $f$ are normal and integral. I am looking for examples of rank $1$, reflexive sheaves on $X$ such that its restriction to the generic fiber is reflexive but its restriction to the special fiber $X_k$ is not a reflexive sheaf on $X_k$. Any hint/reference will be most welcome.
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