In mathematics, and in particular differential geometry and complex geometry, a complex analytic variety or complex analytic space is a generalization of a complex manifold that allows the presence of singularities. Complex analytic varieties are locally ringed spaces that are locally isomorphic to local model spaces, where a local model space is an open subset of the vanishing locus of a finite set of holomorphic functions. == Definition == Denote the constant sheaf on a topological space with value C {\displaystyle \mathbb {C} }...