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

2009/07/27 by Teresa Cortadellas Benítez, Teresa Cortadellas Benitez, Benitez, Teresa Cortadellas +3
Computer Science · Mathematics · #13A30 #14P10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:13A30 #msc:14P10

paper · pdf · doi:10.48550/arxiv.0907.4669

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

openalex publication_date 2009/07/27 · arxiv created 2010/04/07 · arxiv updated 2010/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 parametrizations having a syzygy of minimal degree (μ=1). We also show that our approach can be applied to parametrizations of rational surfaces having a Hilbert-Burch resolution with μ₁=μ₂=1.

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