# Implicitization of tensor product surfaces via virtual projective resolutions

## TL;DR

This paper presents a method to compute the implicit equations of tensor product surfaces in 3D projective space using virtual projective resolutions and syzygies of the base point locus.

## Contribution

It introduces a novel approach leveraging virtual projective resolutions to derive implicit equations for tensor product surfaces.

## Key findings

- Successfully computes implicit equations for specific tensor product surfaces.
- Utilizes syzygies of the base point locus in the implicitization process.
- Provides an explicit construction of virtual projective resolutions.

## Abstract

We derive the implicit equations for certain parametric surfaces in three-dimensional projective space termed tensor product surfaces. Our method computes the implicit equation for such a surface based on the knowledge of the syzygies of the base point locus of the parametrization by means of constructing an explicit virtual projective resolution.