A package for computing implicit equations of parametrizations from toric surfaces

Abstract

In this paper we present an algorithm for computing a matrix representation for a surface in P^3 parametrized over a 2-dimensional toric variety T. This algorithm follows the ideas of [Botbol-Dickenstein-Dohm-09] and it was implemented in Macaulay2. We showed in [BDD09] that such a surface can be represented by a matrix of linear syzygies if the base points are finite in number and form locally a complete intersection, and in [Botbol-09] we generalized this to the case where the base locus is not necessarily a local complete intersection. The key point consists in exploiting the sparse structure of the parametrization, which allows us to obtain significantly smaller matrices than in the homogeneous case.