Normal complex space

Summary

A normal complex space is a complex analytic space whose local rings are integrally closed domains. Normal spaces are reduced, locally irreducible, and their singular locus has codimension at least $2$. On a normal space, the Riemann extension theorem holds: a function that is holomorphic off the singular locus and locally bounded is holomorphic. Every reduced complex space has a normalization, so normal spaces are a standard first step in the study of singularities.