Implicitization of tensor product surfaces via virtual projective resolutions

2019/08/06 by Eliana Duarte, Duarte, Eliana, Alexandra Seceleanu +1
Mathematics · #13P15 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.AG #math.RA #msc:13P15

paper · pdf · doi:10.48550/arxiv.1908.02086

30 pages

arxiv created 2019/08/06 · arxiv updated 2019/08/07

Abstract

We derive the implicit equations for certain parametric surfaces in three-dimensional projective space termed tensor product surfaces. Our method computes the implicit equation for such a surface based on the knowledge of the syzygies of the base point locus of the parametrization by means of constructing an explicit virtual projective resolution.

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