A numerical toolkit for multiprojective varieties

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

Journal:
Math. Comp. **90** (2021), 413-440

MSC (2010):
Primary 65H10

DOI:
https://doi.org/10.1090/mcom/3566

Published electronically:
October 2, 2020

MathSciNet review:
4166467

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Abstract | References | Similar Articles | Additional Information

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.

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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

Keywords:
Numerical algebraic geometry,
multiprojective variety

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.

Article copyright:
© Copyright 2020
American Mathematical Society