Geodesic
On Certain Loci of Hankel $r$-Planes of~$\mathbb P^m$
Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 597-608.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the loci of Hankel $(l+1)$-planes in $\mathbb P^m$ containing a fixed $l$-plane $\pi_l$. We investigate the singular locus of the variety $H(r,m)$ of Hankel $r$-planes in $\mathbb P^m$.
Keywords: Grassmannian, singularities, Hankel variety, projective space, standard rational normal curve
Mots-clés : quadric hypersurface. 
@article{MZM_2012_92_4_a9,
     author = {G. Failla},
     title = {On {Certain} {Loci} of {Hankel} $r${-Planes} of~$\mathbb P^m$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {597--608},
     publisher = {mathdoc},
     volume = {92},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a9/}
}
TY  - JOUR
AU  - G. Failla
TI  - On Certain Loci of Hankel $r$-Planes of~$\mathbb P^m$
JO  - Matematičeskie zametki
PY  - 2012
SP  - 597
EP  - 608
VL  - 92
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a9/
LA  - ru
ID  - MZM_2012_92_4_a9
ER  - 
%0 Journal Article
%A G. Failla
%T On Certain Loci of Hankel $r$-Planes of~$\mathbb P^m$
%J Matematičeskie zametki
%D 2012
%P 597-608
%V 92
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a9/
%G ru
%F MZM_2012_92_4_a9
G. Failla. On Certain Loci of Hankel $r$-Planes of~$\mathbb P^m$. Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 597-608. http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a9/

[1] S. Giuffrida, R. Maggioni, “Hankel Planes”, J. Pure Appl. Algebra, 209:1 (2007), 119–138 | DOI | MR | Zbl

[2] G. Heinig, K. Rost, Algebraic Methods for Toeplitz-like Matrices and Operators, Oper. Theory Adv. Appl., 13, Birkhäuser-Verlag, Basel, 1984 | MR | Zbl

[3] S. Giuffrida, K. Ranestad, “A geometric characterization of Hankel $r$-planes”, Bull. London Math. Soc., 42:5 (2010), 912–916 | DOI | MR | Zbl

[4] G. Failla, S. Giuffrida, “On the Hankel lines variety $H(1,m)\subseteq\mathbb G(1,m)$”, Afr. Diaspora J. Math. (N.S.), 8:2 (2009), 71–79 | MR | Zbl

[5] G. Failla, “On sequences of integers for Hankel $r$-planes in a linear space $\Sigma$ of $\mathbb P^m$”, Matematiche (Catania), 64:1 (2009), 113–125 | MR | Zbl

[6] J. Harris, Algebraic Geometry. A First Course, Grad. Texts in Math., 133, Springer-Verlag, New York, 1992 | MR | Zbl

[7] A. Conca, J. Herzog, G. Valla, “Sagbi bases with applications to blow-up algebras”, J. Reine Angew. Math., 474 (1996), 113–138 | MR | Zbl