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EnglishIn this paper we consider the Segre-Veronese varieties, i.e., the embeddings of products of t projective spaces in the projective space PN via divisors of multi-degree (d1, . . . , dt), and we study the dimension of their higher secant varieties. We give the dimensions of all the higher secant varieties of P1 x P1 embedded by divisors of any bi-degree (d1, d2). We find that Pr x Pk, embedded by divisors of bi-degree (k + 1, 1), has no deficient higher secant varieties, and we give several examples of defective and Grassmann defective Segre-Veronese varieties.
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| Titolo: | Higher Secant Varieties of Segre-Veronese varieties |
| Autori: | |
| Data di pubblicazione: | 2005 |
| Abstract: | In this paper we consider the Segre-Veronese varieties, i.e., the embeddings of products of t projective spaces in the projective space PN via divisors of multi-degree (d1, . . . , dt), and we study the dimension of their higher secant varieties. We give the dimensions of all the higher secant varieties of P1 x P1 embedded by divisors of any bi-degree (d1, d2). We find that Pr x Pk, embedded by divisors of bi-degree (k + 1, 1), has no deficient higher secant varieties, and we give several examples of defective and Grassmann defective Segre-Veronese varieties. |
| Handle: | http://hdl.handle.net/11567/252716 |
| ISBN: | 3110181606 |
| Appare nelle tipologie: | 04.01 - Contributo in atti di convegno |
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