Fano variety

Fano variety

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 mathbb{P}^1 imes mathbb{P}^1 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).


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