C=A \cap B of two complex algebraic sets A and B. Enroute of this result
we first show how to find the irreducible decomposition of system of
polynomial equations restricted to an algebraic set. The intersection of
components of A and B follows by decomposing the diagonal system u-v=0
restricted to (u,v) in A x B.
The talk reports on joined work with Jan Verschelde (Univ. of Illinios at
Chicago) and Charles W. Wampler (General Motors Research and Development).