An anticanonical linear system on a smooth projective variety is the complete linear system 
for a positive integer 
. Its divisors are the zeros of anticanonical plurisections.
For a smooth connected projective complex variety of dimension 
with smoothly semipositive 
, fix a semipositive curvature
form 
,
let 
be its maximum complex rank, and let 
be ample. For a divisor 
,
define 
if 
,
and 
if 
.
A valuation is centered on 
when its valuation ring
dominates a local ring of 
. Divisor orders use local defining rational functions there.
