Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence and thus satisfy stable Harbourne conjecture. In prime characteristic, can take any radical ideal a ring in regular ring, provided its symbolic powers are given saturations with maximal ideal. Although this property is not suitable for reduction to characteristic p, simi...

We prove that in a 2-Calabi-Yau triangulated category, each cluster tilting subcategory is Gorenstein with all its finitely generated projectives of injective dimension at most one. We show that the stable category of its Cohen-Macaulay modules is 3-CalabiYau. We deduce in particular that cluster-tilted algebras are Gorenstein of dimension at most one, and hereditary if they are of finite globa...