Pome

Corollary 11.1.140C9AAEBBC04C

Corollary 11.1.14.0C9AAEBBC04C In general, the total Monge–Ampère mass is not determined by the ordinary singularity type or by the multiplier ideals, even among smooth strictly $\omega $-plurisubharmonic potentials.

Proof. The potentials $u_ t$ of example 11.1.12 are smooth on the compact manifold $X$, so any two of them differ by a bounded function and have the same singularity type in the sense of section 5.33. For the same reason, their multiplier ideals are the structure sheaf for every positive multiple of the weight. By (11.1.13), their masses differ. $\square$

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