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

Details Minimal generators of the defining ideal of the Rees Algebra associated to monoid parametrizations Minimal generators of the defining ideal of the Rees Algebra associated to monoid parametrizations

2009-07-27

arxiv.org/abs/0907.4669v2

Mathematics

Commutative Algebra

17 pages, amsart latex, revised version accepted for publication in the Journal Computer Aided Geometric Design.

Scientific paper

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 parametrizations having a syzygy of minimal degree (\mu=1). We also show that our approach can be applied to parametrizations of rational surfaces having a Hilbert-Burch resolution with \mu_1=\mu_2=1.

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