Fano variety

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In algebraic geometry, a branch of mathematics, a Fano variety is a variety whose anticanonical bundle is ample. Formally, it is a kind of dual to a variety of general type (whose canonical bundle is ample.).

Fano varieties in dimensions 1 and 2 are all rational. In dimension 2 they are called del Pezzo surfaces and are isomorphic to either or to the projective plane blown up in at most 8 general points.

Fano varieties all have Kodaira dimension −∞. They are named for Gino Fano (1871-1952).