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On the Hankel Lines Variety H(1,m)⊆ G(1,m)

Volume 8, Number 2 (2009), 71 - 79

On the Hankel Lines Variety H(1,m)⊆ G(1,m)

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Abstract

In the Grassmannian G(1;m) µ PN of lines of Pm we consider the subvariety H(1;m) of Hankel lines. We find that, for m>3, it is singular along S1(Xm)µG(1;m), corresponding to the cordal variety of the standard rational normal curve Xm µ Pm. Moreover, we describe subvarieties of H(1;m) which are invariant for certain projectivities of PN.