Tangents to an Analytic Variety

Abstract

The purpose of this paper is to study the structure of the sets of tangent vectors and tangent planes to a complex analytic variety, particularly in the neighborhood of singular points of the variety. We prove the existence of a stratification of the variety which has nice properties relative to tangent planes. Corresponding properties of real analytic varieties (which are the real parts of of complex ones) may be found by considering the corresponding complex analytic variety.