The multiplier ideal of a singular Hermitian metric with local squared frame norm 
consists of holomorphic germs 
for which 
is locally integrable.
For plurisubharmonic weights these local ideals form a coherent ideal sheaf.
The inclusion 
means that the canonical section of the effective integral divisor 
has locally integrable
squared norm.
Multiplier Ideal
See also
Coherent Sheaf, Germ, Pseudo-Effective Divisor, Singular Hermitian MetricExplore with Wolfram|Alpha
References
Demailly, J.-P. Analytic Methods in Algebraic Geometry. Somerville, MA: International Press, 2012.Cite this as:
Weisstein, Eric W. "Multiplier Ideal." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MultiplierIdeal.html