A Mori fiber space in the classical minimal model program is a projective morphism 
with connected fibers and 
, where 
is a Q-factorial variety
with terminal singularities, 
is a normal variety, the
relative Picard number is one, and 
is relatively ample. Here 
is the canonical divisor.
Relative Picard number one means that divisors modulo
numerical equivalence on algebraic curves contracted
by 
span a one-dimensional real vector space (Kollár
and Mori 1998). For example, projective space
maps to a point and its negative canonical divisor
is ample.
For a log canonical pair, the analogous endpoint uses 
in place of 
.
A minimal model instead has a nef divisor as its adjoint
divisor.
