Mini-Workshop: Surface Modeling and Syzygies

Abstract

The problem of determining the implicit equation of the image of a rational map φ : P2 99K P3 is of theoretical interest in algebraic geometry, and of practical importance in geometric modeling. There are essentially three methods which can be applied to the problem: Gröbner bases, resultants, and syzygies. Elimination via Gröbner basis methods tends to be computationally intensive and, being a general tool, is not adapted to the geometry of specific problems. Thus, it is primarily the latter two techniques which are used in practice. This is an extremely active area of research where many different perspectives come into play. The mini-workshop brought together a diverse group of researchers with different areas of expertise.