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Mathematics of Computation

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Implicitization of tensor product surfaces via virtual projective resolutions


Authors: Eliana Duarte and Alexandra Seceleanu
Journal: Math. Comp. 89 (2020), 3023-3056
MSC (2010): Primary 13P15; Secondary 13D02, 14Q10
DOI: https://doi.org/10.1090/mcom/3548
Published electronically: June 29, 2020
MathSciNet review: 4136556
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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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Additional Information

Eliana Duarte
Affiliation: Max-Planck-Institute for Mathematics in the Sciences, Leipzig; Otto-von-Guericke Universität, Magdeburg
MR Author ID: 1132228
Email: eliana.duarte@ovgu.de

Alexandra Seceleanu
Affiliation: Mathematics Department, University of Nebraska–Lincoln, Lincoln, Nebraska 68588
MR Author ID: 896988
ORCID: 0000-0002-7929-5424
Email: aseceleanu@unl.edu

Received by editor(s): August 6, 2019
Received by editor(s) in revised form: March 1, 2020
Published electronically: June 29, 2020
Additional Notes: The first author was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)-314838170, GRK2297 MathCoRe.
The second author was supported by NSF grant DMS–1601024 and EpSCOR award OIA–1557417.
Article copyright: © Copyright 2020 Eliana Duarte and Alexandra Seceleanu