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.
A. Gimigliano, M.V. Catalisano, A. Geramita (2005). Higher Secant Varieties of the Segre varieties P1x...xP1. JOURNAL OF PURE AND APPLIED ALGEBRA, 201, 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
