## Implicitization of tensor product surfaces via virtual projective resolutions

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Eliana Duarte and Alexandra Seceleanu
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**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