Real rank boundaries and loci of forms

In this article, we study forbidden loci and typical ranks of forms with respect to the embeddings of given by the line bundles (2, 2d). We introduce the Ranestad-Schreyer locus corresponding to supports of non-reduced apolar schemes. We show that, in those cases, this is contained in the forbidden...

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Bibliographic Details
Published in:Linear & multilinear algebra 2019-07, Vol.67 (7), p.1404-1419
Main Author: Ventura, Emanuele
Format: Article
Language:English
Subjects:
Apolarity
Boundaries
Cases (containers)
hyperdeterminants
Hyperspaces
Loci
real rank
tensors
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Summary:In this article, we study forbidden loci and typical ranks of forms with respect to the embeddings of given by the line bundles (2, 2d). We introduce the Ranestad-Schreyer locus corresponding to supports of non-reduced apolar schemes. We show that, in those cases, this is contained in the forbidden locus. Furthermore, for these embeddings, we give a component of the real rank boundary, the hypersurface dividing the minimal typical rank from higher ones. These results generalize to a class of embeddings of . Finally, in connection with real rank boundaries, we give a new interpretation of the hyperdeterminant.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2018.1454395