  We study birational maps with empty base locus defined by almost complete
intersection ideals. Birationality is shown to be expressed by the equality of
two Chern numbers. We provide a relatively effective method of their
calculation in terms of certain Hilbert coefficients. In dimension two the
structure of the irreducible ideals leads naturally to the calculation of
Sylvester determinants via a computer-assisted method. For degree at most 5 we
produce the full set of defining equations of the base ideal. The results
answer affirmatively some questions raised by D. Cox.
