On the dimension of higher secant varieties of Segre varieties Pn x ... x Pn

• Autores: Tahereh Aladpoosh, Hassan Haghighi
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 215, Nº 5, 2011, págs. 1040-1052
• Idioma: inglés
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• Resumen

  • In this paper we are concerned with the problem of the dimension of the sth higher secant variety of the segre variety P-n x ... x P-n (t-times, t >= 3 and n > 1). in order to determine the dimensions of these varieties we construct a specific subscheme W of P-nt which is a generic configuration of the union of t linear subspaces of dimension n - 1 and s double points, and then we compute the value of Hilbert function of this scheme at degree t. We show that W has the expected Hilbert function at degree t, except possibly for certain n values of s.