A Partial Stratification of Secant Varieties of Veronese Varieties via Curvilinear Subschemes - Ballico, Edoardo; Bernardi, Alessandra (Sarajevo Journal of Mathematics, 2024)
We give a partial "quasi-stratification" of the secant varieties of the order d Veronese variety X_m,d of P^m. It covers the set σ _t(X_m,d)^ of all points lying on the linear span of curvilinear subschemes of X_m,d, but two "quasi-strata" may overlap. For low border rank two different "quasi-strata" are disjoint and we compute the symmetric rank of their elements. Our tool is the Hilbert schemes of curvilinear subschemes of Veronese varieties. To get a stratification we attach to each Pσ _t(X_m,d)^ the minimal label of a quasi-stratum containing it. 2000 Mathematics Subject Classification. 14N05, 15A69