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

https://doi.org/10.1016/j.cagd.2010.04.003Get rights and content

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 (μ=1). We also show that our approach can be applied to parameterizations of rational surfaces having a Hilbert–Burch resolution with μ1=μ2=1.

References (28)

  • Tom Sederberg et al.

    Implicitizing rational curves by the method of moving algebraic curves

    Parametric Algebraic Curves and Applications

    J. Symbolic Comput.

    (1997)
  • Thomas Sederberg et al.

    Approximate implicitization using monoid curves and surfaces

    Graph. Models Image Process.

    (1999)
  • Winfried Bruns et al.

    Cohen–Macaulay Rings

    (1993)
  • Laurent Busé et al.

    Torsion of the symmetric algebra and implicitization

    Proc. Amer. Math. Soc.

    (2009)
  • Cited by (0)

    Both authors are supported by the Research Project MTM2007–67493 from the Ministerio de Ciencia e Innovación, Spain.

    View full text