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- W2950935836 abstract "Let $Gr(k,n)$ be the Plucker embedding of the Grassmann variety of projective $k$-planes in $P n$. For a projective variety $X$, let $sigma_s(X)$ denote the variety of its $s-1$ secant planes. More precisely, $sigma_s(X)$ denotes the Zariski closure of the union of linear spans of $s$-tuples of points lying on $X$. We exhibit two functions $s_0(n)le s_1(n)$ such that $sigma_s(Gr(2,n))$ has the expected dimension whenever $ngeq 9$ and either $sle s_0(n)$ or $s_1(n)le s$. Both $s_0(n)$ and $s_1(n)$ are asymptotic to $frac{n^2}{18}$. This yields, asymptotically, the typical rank of an element of $wedge^{3} 1pt {mathbb C}^{n+1}$. Finally, we classify all defective $sigma_s(Gr(k,n))$ for $sle 6$ and provide geometric arguments underlying each defective case." @default.
- W2950935836 created "2019-06-27" @default.
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- W2950935836 date "2009-01-17" @default.
- W2950935836 modified "2023-09-27" @default.
- W2950935836 title "Non-Defectivity of Grassmannians of planes" @default.
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