Abstract: Noma developed the inner projection method and gave a classification of projective varieties in a sense. As an important consequence, he established a sharp linear bound for Castelnuovo-Mumford regularity of structure sheaves on smooth projective varieties of arbitrary dimension. I will show how blending Noma’s classification with multiplier ideal theory leads to the same bound for normal projective varieties with at worst isolated Q-Gorenstein singularities. By contrast, it is known only recently that such a bound fails for varieties with arbitrary singularities. This is based on a joint work with J. Moraga and J. Park.