Strength and slice rank of forms are generically equal

We prove that strength and slice rank of homogeneous polynomials of degree d ≥ 5 over an algebraically closed field of characteristic zero coincide generically. To show this, we establish a conjecture of Catalisano, Geramita, Gimigliano, Harbourne, Migliore, Nagel and Shin concerning dimensions of s...

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Bibliographic Details
Published in:Israel journal of mathematics 2023-04, Vol.254 (1), p.275-291
Main Authors: Ballico, Edoardo, Bik, Arthur, Oneto, Alessandro, Ventura, Emanuele
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Polynomials
Theoretical
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Summary:We prove that strength and slice rank of homogeneous polynomials of degree d ≥ 5 over an algebraically closed field of characteristic zero coincide generically. To show this, we establish a conjecture of Catalisano, Geramita, Gimigliano, Harbourne, Migliore, Nagel and Shin concerning dimensions of secant varieties of the varieties of reducible homogeneous polynomials. These statements were already known in degrees 2 ≤ d ≤ 7 and d = 9.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-022-2397-0