Special effect varieties in higher dimension.

Cristiano Bocci

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We present a class of toric varieties V which, over any algebraically closed field of characteristic zero, are defined by codim V +1 binomial equations.

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Segre-Veronese embeddings of P x P x P and their secant varieties.

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In this paper we compute the dimension of all the s higher secant varieties of the Segre-Veronese embeddings Y of the product P × P × P in the projective space P via divisors of multidegree d = (a,b,c) (N = (a+1)(b+1)(c+1) - 1). We find that Y has no deficient higher secant varieties, unless d = (2,2,2) and s = 7, or d = (2h,1,1) and s = 2h + 1, with defect 1 in both cases.