| Abstract: Suppose that X is an algebraic manifold
and D_1, ..., D_h 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 : X_1 -> X
such that IO_{X_1} is locally generated by a single equation, where I is
the ideal generated by the D'_i, where D'_i is the strict transform of
D_i.
In this talk, 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. |
