Canonical Divisor

A canonical divisor on a normal variety over a field of characteristic zero is the Weil divisor of a nonzero rational differential form of top degree on its smooth locus. Different choices give linearly equivalent Weil divisors, so the canonical divisor class is well-defined. On a smooth variety, it represents the canonical bundle (Kollár and Mori 1998).

The canonical divisor controls birational classification. The minimal model program seeks a birational model on which , or an adjoint divisor , is a nef divisor.