When does the subadditivity theorem for multiplier ideals hold?

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66096Demailly, Ein and Lazarsfeld \cite{DEL} proved the subadditivity theorem for multiplier ideals, which states the multiplier ideal of the product of ideals is contained in the product of the individual multiplier ideals, on non-singular varieties. We prove that, in two-dimensional case, the subadditivity theorem holds on log-terminal singularities. However, in higher dimensional case, we have several counter-examples. We consider the subadditivity theorem for monomial ideals on toric rings, and construct a counter-example on a three-dimensional toric ring.12 pages, AMS-LaTeX; v.2: minor changes, to appear in Trans. Amer. Math. SocCommutative AlgebraAlgebraic Geometry13B22; 14J17When does the subadditivity theorem for multiplier ideals hold?text