irreducible component

Let GN be an open set.


A locally analytic set (or an analytic variety) VG is said to be irreducible if whenever we have two locally analytic sets V1 and V2 such that V=V1V2, then either V=V1 or V=V2. Otherwise V is said to be . A maximal irreducible subvariety of V is said to be an irreducible componentPlanetmathPlanetmath of V. Sometimes irreducible components are called ircomps.

Note that if V is an analytic variety in G, then a subvariety W is an irreducible component of V if and only if W* (the set of regular pointsMathworldPlanetmath of W) is a connected complex analytic manifold. This means that the irreducible components of V are the closuresPlanetmathPlanetmath of the connected componentsPlanetmathPlanetmath of V*.


  • 1 Hassler Whitney. . Addison-Wesley, Philippines, 1972.
Title irreducible component
Canonical name IrreducibleComponent1
Date of creation 2013-03-22 15:04:58
Last modified on 2013-03-22 15:04:58
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 5
Author jirka (4157)
Entry type Definition
Classification msc 32C25
Classification msc 32A60
Synonym ircomp
Related topic AnalyticSet
Defines irreducible analytic variety
Defines irreducible locally analytic set
Defines irreducible analytic variety
Defines reducible locally analytic set
Defines reducible analytic variety