Minimal generators of the defining ideal of the Rees Algebra associated to monoid parameterizations

Authors:
Teresa Cortadellas Benítez;Carlos D'Andrea
Affiliations:
Universitat de Barcelona, Departament d'Àlgebra i Geometria, Gran Via 585, E-08007 Barcelona, Spain;Universitat de Barcelona, Departament d'Àlgebra i Geometria, Gran Via 585, E-08007 Barcelona, Spain
Venue:
Computer Aided Geometric Design
Year:
2010

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Abstract

We describe a minimal set of generators of the defining ideal of the Rees Algebra associated to a proper parametrization of any monoid hypersurface. In the case of plane curves, we recover a known description for rational parameterizations having a syzygy of minimal degree (@m=1). We also show that our approach can be applied to parameterizations of rational surfaces having a Hilbert-Burch resolution with @m"1=@m"2=1.