Implicitizing rational hypersurfaces using approximation complexes

Details Implicitizing rational hypersurfaces using approximation complexes Implicitizing rational hypersurfaces using approximation complexes

2003-01-21

arxiv.org/abs/math/0301238v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as determinants of certain graded parts of a so-called approximation complex. We detail and improve this method by providing an in-depth study of the cohomology of such a complex. In both particular cases of interest of curve and surface implicitization we also yield explicit algorithms which only involves linear algebra routines.

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