Ela Some Subspaces of the Projective Space
نویسنده
چکیده
Let V be a 2m-dimensional vector space over a field F (m ≥ 2) and let k ∈ {1, . . . , 2m − 1}. Let A2m−1,k denote the Grassmannian of the (k − 1)-dimensional subspaces of PG(V ) and let egr denote the Grassmann embedding of A2m−1,k into PG( ∧k V ). Let S be a regular spread of PG(V ) and let XS denote the set of all (k − 1)-dimensional subspaces of PG(V ) which contain at least one line of S. Then we show that there exists a subspace Σ of PG( ∧k V ) for which the following holds: (1) the projective dimension of Σ is equal to ( 2m k )
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