nLab
analytic variety

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 December 20, 2012 04:17:49 by Urs Schreiber (82.169.65.155)