Hi all:
I have a geometry question. Given an ALGEBRAIC variety V in CC^n
defined by a single polynomial and given a point p in V, how do you
compute the number of (distinct) irreducible ANALYTIC components of V
passing through p?
For example, let f = y^2 -x^2*(1 +x). Then the variety V(f) has two
irreducible analytic components passing through (0,0), one for each
factor of the decomposition
f = (y -x*sqrt(1+x)) *(y +x*sqrt(1+x))
in CC{x,y}, the ring of power series convergent in a neighborhood of
(0,0).
Alex
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