Semi-Log Canonical Pair

A semi-log canonical pair is a possibly nonnormal pair whose normalization with its conductor boundary and pulled-back boundary is log canonical. More precisely, is reduced, equidimensional, seminormal, satisfies Serre's condition S₂, and has only nodes in codimension one. The rational divisor is effective, has no component in the nonnormal locus, and makes rational Cartier. If is the normalization and the reduced conductor divisor on defined by the pulled-back conductor ideal, the defining condition is that is log canonical. This is often abbreviated slc.

A normal log canonical pair is a semi-log canonical pair. The conductor records where normalization components are joined, and sections on those components must agree there to descend to . The definition permits nodal curves, whose normalization is smooth and has reduced conductor boundary.