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Ranks and symmetric ranks of cubic surfaces

Abstract:

We study cubic surfaces as symmetric tensors of format 4 × 4 × 4. We consider the non-symmetric tensor rank and the symmetric Waring rank of cubic surfaces, and show that the two notions coincide over the complex numbers. The corresponding algebraic problem concerns border ranks. We show that the non-symmetric border rank coincides with the symmetric border rank for cubic surfaces. As part of our analysis, we obtain minimal ideal generators for the symmetric analogue to the secant variety fro...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.jsc.2019.10.001

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Institution:
University of Oxford
Department:
Mathematical Institute
Role:
Author
Publisher:
Elsevier
Journal:
Journal of Symbolic Computation More from this journal
Volume:
101
Pages:
304-317
Publication date:
2019-10-10
Acceptance date:
2019-10-03
DOI:
ISSN:
0747-7171
Language:
English
Keywords:
Pubs id:
pubs:1061510
UUID:
uuid:fe4aa034-e1b0-4e7c-b592-d93e869e8f5b
Local pid:
pubs:1061510
Source identifiers:
1061510
Deposit date:
2019-10-10

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