On the X-rank with Respect to Linear Projections of Projective Varieties
نویسندگان
چکیده
ABSTRACT: In this paper we improve the known bound for the X-rank RX(P ) of an element P ∈ PN in the case in which X ⊂ Pn is a projective variety obtained as a linear projection from a general v-dimensional subspace V ⊂ Pn+v . Then, if X ⊂ Pn is a curve obtained from a projection of a rational normal curve C ⊂ Pn+1 from a point O ⊂ Pn+1, we are able to describe the precise value of the X-rank for those points P ∈ Pn such that RX(P ) ≤ RC(O) − 1 and to improve the general result. Moreover we give a stratification, via the X-rank, of the osculating spaces to projective cuspidal projective curves X. Finally we give a description and a new bound of the X-rank of subspaces both in the general case and with respect to integral non-degenerate projective curves.
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