Non-defectivity of Grassmannians of planes
By Hirotachi Abo, Giorgio Ottaviani, C. Peterson. 2009
47 citations recorded by the source corpus.
Let Gr(k,n) be the Plucker embedding of the Grassmann variety of projective k-planes in Pn. For a projective variety X, lets(X) denote the variety of its s 1 secant planes. More precisely, �s(X) denotes the Zariski closure of the union of linear spans of s-tuples of points lying on X. We exhibit two functions s0(n) � s1(n) such thats(Gr(2,n)) has the expected dimension whenever n � 9 and either ss0(n) or s1(n) � s. Both s0(n) and s1(n) are asymptotic to n 2 18 . This yields, asymptotically, the typical rank of an element of ^ 3 C n+1 . Finally, we classify all defectives(Gr(k,n)) for s � 6 and provide geometric arguments underlying each defective case.
Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/5bf817a776bf43d35f0fe1e6cc8a4ef990a67142
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In Artificial Intelligence
In Discrete Mathematics and Combinatorics
In Electrical and Electronic Engineering
Citations in the corpus
- The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition (2018, background): “A few more results on non-defectivity are proven in [111, 110].”