nLab analytic variety

Context

Analytic geometry

analytic geometry (complex, rigid, global)

Basic concepts

analytic function

analytification

GAGA

complex geometry

Analytic varieties

Idea

Analytic varieties form an analogue of algebraic varieties in analytic context; they are more general than analytic manifolds in allowing singularities.

While an algebraic variety is the loci of zeros of some set of polynomials, an analytic varieties is the loci of zeros of some set of analytic functions. By Chow's theorem every complex projective analytic variety is algebraic; this is based on the machinery of Weierstrass (the Weierstrass preparation theorem etc.).

Literature

• P. Griffiths, J. Harris, Principles of algebraic geometry

Revised on June 12, 2014 13:39:42 by :)? (186.105.146.195)