We show that the compatibility of the relative canonical sheaf with base change fails generally in families of normal varieties. Furthermore, it always fails if the general fiber of a family of pure dimension is Cohen–Macaulay and the special fiber contains a strictly point. In particular, in moduli spaces with functorial relative canonical sheaves Cohen–Macaulay schemes can not degenerate to schemes. Another, less immediate consequence is that the canonical sheaf of an , scheme of pure dimension is not .
"Base change behavior of the relative canonical sheaf related to higher dimensional moduli." Algebra Number Theory 7 (2) 353 - 378, 2013. https://doi.org/10.2140/ant.2013.7.353