# On the homology of two-dimensional elimination

## TL;DR

This paper investigates the homology of two-dimensional elimination by analyzing birational maps defined by almost complete intersection ideals, providing new methods for calculating Chern numbers and explicit equations for base ideals.

## Contribution

It introduces an effective method to compute Chern numbers using Hilbert coefficients and determines the defining equations of base ideals for degrees up to 5.

## Key findings

- Birationality characterized by equality of two Chern numbers.
- Provided a computational approach for Sylvester determinants.
- Full set of defining equations for base ideals of degree ≤ 5.

## Abstract

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.