Computing $A$-resultants via direct images

TL;DR

This paper presents a new algorithm for computing A-resultants on toric varieties that is more efficient and feasible, avoiding Gr"obner basis computations, thus advancing computational algebraic geometry.

Contribution

It introduces a novel algorithm for direct image computation of complexes on toric varieties, improving the practicality of Weyman's method for A-resultants.

Findings

Algorithm is computationally feasible and effective.

Avoids Gr"obner basis computations entirely.

Enhances the computation of A-resultants for specific monomial supports.

Abstract

We improve a previously known theoretic method to compute A-resultants for suitable monomial support sets due to Weyman to the extent that it becomes computationally feasible and effective. This is achieved by introducing a new algorithm for the computation of direct images of complexes of coherent sheaves on toric varieties. The procedure does not rely on Gr\"obner basis computations at any stage.