We characterize for any d the d-uple Veronese embedding of P^n as the only variety that, under certain general conditions, can be projected from the Grassmannian of (d-1)-planes in P^(nd+d-1) to the Grassmannian of (d-1)-planes in P^(n+2d-3) in such a way that two (d-1)-planes meet at most in one point. We also study the relation of this problem with the Steiner bundles over P^n.
Characterization of Veronese varieties via projections in Grassmannians / E.Arrondo; R.Paoletti. - STAMPA. - (2005), pp. 1-12.
Characterization of Veronese varieties via projections in Grassmannians
PAOLETTI, RAFFAELLA
2005
Abstract
We characterize for any d the d-uple Veronese embedding of P^n as the only variety that, under certain general conditions, can be projected from the Grassmannian of (d-1)-planes in P^(nd+d-1) to the Grassmannian of (d-1)-planes in P^(n+2d-3) in such a way that two (d-1)-planes meet at most in one point. We also study the relation of this problem with the Steiner bundles over P^n.
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