Abstract:In this paper, we prove a rough characterization for G k−1,k -defective n-dimensional non-degenerate varieties X ⊂ P N if k n. In the case of smooth surfaces or threefolds, we give a fine classification.
We give a rough characterization for n-dimensional varieties with G k−1 k -defect equal to a > 0 if k ≥ n. Then we apply this in the case that a ≥ n − 2 to become a fine classification.
We give a rough characterization for n-dimensional varieties with G k−1 k -defect equal to a > 0 if k ≥ n. Then we apply this in the case that a ≥ n − 2 to become a fine classification.
We consider the dimensions of the higher secant varieties of the Grassmann varieties. We give new instances where these secant varieties have the expected dimension and also a new example where a higher secant variety does not.
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