Let V_t be image of the Segre embedding of P1x...xP1 (t-copies) and let (V_t)^s be its s-secant variety, which is the closure of the union of all the (s-1)-planes which are s-secant to V_t. The expected dimension of (V_t)^s is min {st+(s-1),2^t-1} . This is not the case for (V?4)^3, which we conjecture is the only defective example in this infinite family. We prove (Theorem 2.3)that under certain conditions on t,s (which leave only one value of s uncovered for all t) that the expected dimension is actually achieved.

Higher Secant Varieties of the Segre varieties P1x...xP1 / A. Gimigliano; M.V. Catalisano; A. Geramita. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - STAMPA. - 201:(2005), pp. 367-380. [10.1016/j.jpaa.2004.12.049]

Higher Secant Varieties of the Segre varieties P1x...xP1

GIMIGLIANO, ALESSANDRO;A. Geramita
2005

Abstract

Let V_t be image of the Segre embedding of P1x...xP1 (t-copies) and let (V_t)^s be its s-secant variety, which is the closure of the union of all the (s-1)-planes which are s-secant to V_t. The expected dimension of (V_t)^s is min {st+(s-1),2^t-1} . This is not the case for (V?4)^3, which we conjecture is the only defective example in this infinite family. We prove (Theorem 2.3)that under certain conditions on t,s (which leave only one value of s uncovered for all t) that the expected dimension is actually achieved.
2005
Higher Secant Varieties of the Segre varieties P1x...xP1 / A. Gimigliano; M.V. Catalisano; A. Geramita. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - STAMPA. - 201:(2005), pp. 367-380. [10.1016/j.jpaa.2004.12.049]
A. Gimigliano; M.V. Catalisano; A. Geramita
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/27442
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