## A numerical toolkit for multiprojective varieties

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Jonathan D. Hauenstein, Anton Leykin, Jose Israel Rodriguez and Frank Sottile
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## Abstract:

A numerical description of an algebraic subvariety of projective space is given by a general linear section, called a witness set. For a subvariety of a product of projective spaces (a multiprojective variety), the corresponding numerical description is given by a witness collection, whose structure is more involved. We build on recent work to develop a toolkit for the numerical manipulation of multiprojective varieties that operates on witness collections and to use this toolkit in an algorithm for numerical irreducible decomposition of multiprojective varieties. The toolkit and decomposition algorithm are illustrated throughout in a series of examples.## References

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## Additional Information

**Jonathan D. Hauenstein**- Affiliation: Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46556
- MR Author ID: 832839
- ORCID: 0000-0002-9252-8210
- Email: hauenstein@nd.edu
**Anton Leykin**- Affiliation: School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, Georgia 30332-0160
- MR Author ID: 687160
- ORCID: 0000-0002-9216-3514
- Email: leykin@math.gatech.edu
**Jose Israel Rodriguez**- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- ORCID: 0000-0003-3140-9944
- Email: Jose@math.wisc.edu
**Frank Sottile**- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- MR Author ID: 355336
- ORCID: 0000-0003-0087-7120
- Email: sottile@math.tamu.edu
- Received by editor(s): August 6, 2019
- Received by editor(s) in revised form: April 23, 2020
- Published electronically: October 2, 2020
- Additional Notes: The research of the first author was supported in part by NSF grant CCF-1812746.

The research of the second author was supported in part by NSF grant DMS-1151297.

The research of the third author was supported in part by NSF grant DMS-1402545.

The research of the fourth author was supported in part by NSF grant DMS-1501370. - © Copyright 2020 American Mathematical Society
- Journal: Math. Comp.
**90**(2021), 413-440 - MSC (2010): Primary 65H10
- DOI: https://doi.org/10.1090/mcom/3566
- MathSciNet review: 4166467