In algebraic geometry

Algebraic geometry

Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...

, a Fano fibration or Fano fiber space, named after Gino Fano

Gino Fano

Gino Fano was an Italian mathematician. He was born in Mantua, Italy and died in Verona, Italy.Fano worked on projective and algebraic geometry; the Fano plane, Fano fibration, Fano surface, and Fano varieties are named for him....

, is a morphism of varieties whose general fiber is a Fano variety

Fano variety

In algebraic geometry, a Fano variety, introduced by , is a non-singular complete variety whose anticanonical bundle is ample.Fano varieties are quite rare, compared to other families, like Calabi–Yau manifolds and general type surfaces....

 (in other words has ample anticanonical bundle) of positive dimension. The ones arising from extremal contractions in the minimal model program are called Mori fibrations or Mori fiber spaces. They appear as standard forms for varieties without a minimal model.