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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Implicitization of tensor product surfaces via virtual projective resolutions
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by Eliana Duarte and Alexandra Seceleanu HTML | PDF
Math. Comp. 89 (2020), 3023-3056

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.
References
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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.
  • © Copyright 2020 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
  • MathSciNet review: 4136556