The n -sided toric patches and A -resultants Original Research Article

The aim of this article is to describe a representation of the A -resultant as a single determinant, and to express this resultant as a polynomial in 3×3 determinants. This representation is a generalization of the classical Dixon resultant for three bivariate polynomials of bidegree (m,n) . Using A -resultants we can find implicit equations for Hirzebruch surfaces Fn , n∈N , cyclides, Warren hexagons and toric pentagons. The algorithm has some advantages. It is fast, simple and for the mentioned surfaces can be easily computed using for example the MAPLE package.