A numerical toolkit for multiprojective varieties

Hauenstein, Jonathan; Leykin, Anton; Rodriguez, Jose; Sottile, Frank

doi:10.1090/mcom/3566

A numerical toolkit for multiprojective varieties
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by Jonathan D. Hauenstein, Anton Leykin, Jose Israel Rodriguez and Frank Sottile HTML | PDF

Math. Comp. 90 (2021), 413-440 Request permission

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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