The sparse resultant of an unmixed bivariate system

Amit Khetan (Mathematics, Berkeley)

We give an explicit formula for computing the resultant of any sparse unmixed bivariate system with given support. We construct square matrices whose determinant is exactly the resultant. The matrices are of hybrid Sylvester and Bezout type. Previous work by D'Andrea and Emiris and Canny gave pure Sylvester matrices for sparse resultants of any dimension. In the bivariate case, D'Andrea and Emiris constructed hybrid matrices with one Bezout row. These matrices, however, are only guaranteed to have determinant a nontrivial multiple of the resultant. The main contribution of our paper is the addition of new Bezout terms allowing us to achieve exact formulas. We make use of the exterior algebra techniques of Eisenbud, Floystad, and Schreyer.