On Waring's problem for several algebraic forms

• Autores: Enrico Carlini, Jaydeep V. Chipalkatti
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 78, Nº 3, 2003, págs. 494-517
• Idioma: inglés
• DOI: 10.1007/s00014-003-0769-6
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• Resumen

  • We reconsider the classical problem of representing a finite number of forms of degree d in the polynomial ring over n + 1 variables as scalar combinations of powers of linear forms. We define a geometric construct called a 'grove', which, in a number of cases, allows us to determine the dimension of the space of forms which can be so represented for a fixed number of summands. We also present two new examples, where this dimension turns out to be less than what a naïve parameter count would predict