On the homology of two-dimensional elimination

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.