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 1565-8511. - -:(In corso di stampa).
Strength and slice rank of forms are generically equal
Ballico, Edoardo;Oneto, Alessandro;
In corso di stampa
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.File in questo prodotto:
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