Reduced complex space

Summary

A reduced complex space is a complex analytic space whose structure sheaf has no nonzero nilpotent germs. On such a space, a function is determined by its values at points, so the structure sheaf is a sheaf of genuine complex-valued functions. Reduced complex spaces are the same as complex analytic varieties with their sheaves of holomorphic functions. Every complex space has a reduction, a reduced complex space with the same underlying topological space.