The log discrepancy of a prime divisor over a normal variety measures its coefficient after pulling
back a log canonical divisor. For a pair 
with rationally Cartier 
, choose a smooth birational model 
containing the prime
divisor 
and compatible canonical divisors. Then
 |
It is independent of the chosen higher model. A pair is log canonical if all these values are nonnegative, and Kawamata log terminal
if all are strictly positive. The condition 
-log canonical requires all primitive prime-divisor values
to be at least 
.
Orders and discrepancies can be extended homogeneously to positive real multiples of valuations. A lower bound on singularities is imposed on primitive divisor orders, since arbitrary positive rescaling changes the discrepancy.
