The canonical bundle formula expresses the adjoint divisor of a log-trivial fibration in terms of canonical, discriminant, and moduli data on its base. For a projective
contraction 
of normal varieties, assume 
is an effective rational divisor, 
is a log canonical
pair over the generic point of 
, and 
for a rational Cartier divisor 
. Then the formula is
 |
The coefficient of a prime divisor 
in 
is 
, where 
is the log canonical
threshold of the pullback of 
over its generic point. The remaining rational divisor 
is the moduli part (Han et al. 2022). Tracing these divisors on all birational
models gives b-divisors. Semiampleness of the moduli
b-divisor is the b-semiampleness
conjecture.
