We know, if $π : X → S$ is a generically smooth family of complex projective
varieties, such that $X\_0 := π^{−1}(0)$ is an snc divisor in $X$, then the
monodromy representation is unipotent. Now assume the monodromy representation is unipotent, then is the central fibre $X\_0 := π^{−1}(0)$ simple normal crossing?



If monodromy representation is unipotent then special fiber is snc?
Just to be clear, the local monodromy is unipotent if $X\_0$ is *reduced* with simple normal crossings (that's probably what you meant). As Piotr pointed out, your question, as originally formulated, has an easy negative answer. However, as he suggested, the question can be modified to a something more reasonable:



> 
> If the local monodromy is unipotent, does there exist a birational model with $X\_0$ reduced snc? 
> 
> 
> 


I think this is also no. Take a Lefschetz pencil of sextics $Y\to S=\mathbb{P}^1$ in $\mathbb{P}^4$, so that $Y\_0$ has a node $p$ and no other singularities. By the Picard-Lefschetz formula, the local monodromy is unipotent. Let $X\to S$ be a birational model with $X\_0$ snc. We have a morphism $X\to Y$ given by the relative canonical map. This will dominate the blow up $Bl\_pY$. The exceptional divisor of $Bl\_pY\to Y$ will have multiplicity $2$. So that the components of $X\_0$ lying over this also have multiplicity at least $2$.


