In this paper we improve the known bound for the X-rank R X (P ) of an element P ∈ PN in the case where 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 R X (P ) ≤ R C (O) − 1 and to improve the general result. We also give a stratification, via the X-rank, of the osculating spaces to projective cuspidal projective curves X. 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. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
On the X-rank with respect to linear projections of projective varieties / Ballico, Edoardo; Bernardi, Alessandra. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - STAMPA. - 284:17-18(2011), pp. 2133-2140. [10.1002/mana.200910275]
On the X-rank with respect to linear projections of projective varieties
Ballico, Edoardo;Bernardi, Alessandra
2011-01-01
Abstract
In this paper we improve the known bound for the X-rank R X (P ) of an element P ∈ PN in the case where 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 R X (P ) ≤ R C (O) − 1 and to improve the general result. We also give a stratification, via the X-rank, of the osculating spaces to projective cuspidal projective curves X. 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. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimFile | Dimensione | Formato | |
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