Let $X$ be a smooth, proper scheme and $U\subset X$ be a normal and locally closed subscheme. Let $V\subset X$ be an open dense subscheme such that $U\subset V$ and $X\setminus V$ is a normal crossing divisor. What can I say about the boundary of the closure $\bar{U}$ of $U$ in $X$? Is $\bar{U}$ still normal?
Thx