Strength and slice rank of forms are generically equal

2021/02/23 by Ballico, Edoardo, Bik, Arthur, Oneto, Alessandro +1 · 4 citations
#13A02 #14R20 #15A21 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.11549

Abstract

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.

Cited by

• Isotropy and completeness indices of multilinear maps
• Extremal constructions for apex partite hypergraphs
• Polynomials of small slice rank and strength
• Slice rank and partition rank of the determinant

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