Geometry of Syzygies via Poncelet Varieties

@article{Ilardi2009,
abstract = {We consider the Grassmannian $\mathbb\{G\}r(k,n)$ of $(k+1)$-dimensional linear subspaces of $V_\{n\} = H^\{0\} (\mathbb\{P\}^\{1\}, \mathcal\{O\}_\{\mathbb\{P\}_\{1\}\} (n))$. We define $\mathfrak\{X\}_\{k,r,d\}$ as the classifying space of the $k$-dimensional linear systems of degree $n$ on $\mathbb\{P\}^\{1\}$, whose bases realize a fixed number $r$ of polynomial relations of fixed degree $d$, say $r$ syzygies of degree $d$. Firstly, we compute the dimension of $\mathfrak\{X\}_\{k,r,d\}$. In the second part we make a link between $\mathfrak\{X\}_\{k,r,d\}$ and the Poncelet varieties. In particular, we prove that the existence of linear syzygies implies the existence of singularities on the Poncelet varieties.},
author = {Ilardi, Giovanna, Supino, Paola, Vallès, Jean},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {579-589},
publisher = {Unione Matematica Italiana},
title = {Geometry of Syzygies via Poncelet Varieties},
url = {http://eudml.org/doc/290555},
volume = {2},
year = {2009},
}

TY - JOUR
AU - Ilardi, Giovanna
AU - Supino, Paola
AU - Vallès, Jean
TI - Geometry of Syzygies via Poncelet Varieties
JO - Bollettino dell'Unione Matematica Italiana
DA - 2009/10//
PB - Unione Matematica Italiana
VL - 2
IS - 3
SP - 579
EP - 589
AB - We consider the Grassmannian $\mathbb{G}r(k,n)$ of $(k+1)$-dimensional linear subspaces of $V_{n} = H^{0} (\mathbb{P}^{1}, \mathcal{O}_{\mathbb{P}_{1}} (n))$. We define $\mathfrak{X}_{k,r,d}$ as the classifying space of the $k$-dimensional linear systems of degree $n$ on $\mathbb{P}^{1}$, whose bases realize a fixed number $r$ of polynomial relations of fixed degree $d$, say $r$ syzygies of degree $d$. Firstly, we compute the dimension of $\mathfrak{X}_{k,r,d}$. In the second part we make a link between $\mathfrak{X}_{k,r,d}$ and the Poncelet varieties. In particular, we prove that the existence of linear syzygies implies the existence of singularities on the Poncelet varieties.
LA - eng
UR - http://eudml.org/doc/290555
ER -