Let $A$ be an integral domain which is finitely generated as a $k$-algebra and let $I\subset A$ be an ideal. Let $B$ be its integral closure (in the fraction field $\mathrm{Frac}\ A$) - in this case $B$ is finite as an $A$-module and a finitely generated $k$-algebra.
Are there any relations between the associated primes of $I$ and the associated primes of $IB$ (as an ideal in $B$)?
For example, I'd expect that the number of minimal primes is the same in both cases, but is this true for embedded primes also?