The minimal model program is a procedure in birational algebraic geometry that simplifies a projective algebraic
variety by contractions and flips directed by its canonical divisor, or by the adjoint divisor 
of a log
canonical pair. A divisorial contraction contracts a divisor, while a flip
replaces a contraction that contracts no divisor by another birational model on which
the adjoint divisor is relatively positive (Kollár and Mori 1998).
The intended endpoint is either a minimal model, whose adjoint divisor is a nef divisor, or a Mori fiber space. On smooth
projective surfaces, the classical procedure contracts
smooth rational algebraic curves of self-intersection
.
A good minimal model has a semiample adjoint, so it gives a stronger conclusion than a nef endpoint alone.
