Expressing a general form as a sum of determinants

• Autores: Luca Chiantini , Anthony V. Geramita
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 66, Fasc. 2, 2015, págs. 227-242
• Idioma: inglés
• DOI: 10.1007/s13348-014-0117-8
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• Resumen

  • Let ?=(???) be a non-negative integer ?×? matrix. ? is a homogeneous matrix if ???+???=???+??? for any choice of the four indexes. We ask: If ? is a homogeneous matrix and if ? is a form in ℂ[?1,…??] with ???(?)=trace(?) , what is the least integer, ?(?) , so that ?=????1+⋯+?????(?) , where the ??=(????) are ?×? matrices of forms and ???????=??? for every 1≤?≤?(?) ? We consider this problem for ?≥4 and we prove that ?(?)≤??−3 and ?(?)