In this paper we consider the Segre-Veronese varieties, i.e., the embeddings of P"1 x o x Pn* in the projective space ?N via divisors of multi-degree (di,dt), (N = H(di^""i)), 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 (di,^). We find that Pr x Pfc, embedded by divisors of bi-degree (A; + f, 1), has no deficient higher secant varieties, and we give several examples of defective and Grassmann defective Segre-Veronese varieties.
展开▼
机译：在本文中，我们考虑了Segre-Veronese品种，即P“1 XOX PN *在投影空间中的嵌入，通过多度（di，dt）的二数（n = h（di ^”） ）），我们研究了较高的割线品种的尺寸。我们赋予所有BI度（DI，^）嵌入的P1 x P1的所有较高云含量的尺寸。我们发现PR X PFC，嵌入式通过双程度（A; + F，1）的除数，没有缺乏较高的云的品种，我们提供了若干有缺陷和基层有缺陷的Segre-Veronese品种的例子。
展开▼
