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.

Strength and slice rank of forms are generically equal / Ballico, Edoardo; Bik, Arthur; Oneto, Alessandro; Ventura, Emanuele. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 254:(2023), pp. 275-291. [10.1007/s11856-022-2397-0]

Strength and slice rank of forms are generically equal

Ventura, Emanuele
2023

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2958010