| Suppose that X is an algebraic manifold and D1,...,Dh are effective divisors with simple normal crossings. A basic result in the area of Resolution of Singularities is that there exists a sequence of blow-ups with non-singular centers pi : X1 → X such that IOX1 is locally generated by a single equation, where I is the ideal generated by the Di and D'i is a simple normal crossing divisor, where D'i is the strict transform of Di.; In this paper, we present an extremely simple and canonical proof of this result for varieties of dimension n using an easily computed invariant. The invariant determines a unique subvariety to blow-up and decreases after a single blow-up. |
