Abstract
The trace test in numerical algebraic geometry verifies the completeness of a witness set of an irreducible variety in affine or projective space. We give a brief derivation of the trace test and then consider it for subvarieties of products of projective spaces using multihomogeneous witness sets. We show how a dimension reduction leads to a practical trace test in this case involving a curve in a low-dimensional affine space.
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Research of Leykin supported in part by NSF grants DMS-1151297 and DMS-1719968. Research of Rodriguez supported in part by NSF Grant DMS-1402545. Research of Sottile supported in part by NSF Grant DMS-1501370.
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Leykin, A., Rodriguez, J.I. & Sottile, F. Trace Test. Arnold Math J. 4, 113–125 (2018). https://doi.org/10.1007/s40598-018-0084-3
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DOI: https://doi.org/10.1007/s40598-018-0084-3