Let $R$ be a local (Noetherian) integral domain of dimension greater than one. Can the integral closure (i.e. normalization) of $R$ have a maximal ideal of height one?



Can height one maximal ideals in the normalization contract to non-height one primes in the base?
Example 2 of Appendix A1 of Nagata's "Local Rings" with $m = 0$ is an example of such a ring.


