Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of syzygies via Poncelet varieties   We consider the Grassmannian $\mathbb{G}r(k,n)$ of $(k+1)$-dimensional linear
subspaces of $V_n=H^0({\P^1},\O_{\P^1}(n))$. We define $\frak{X}_{k,r,d}$ as
the classifying space of the $k$-dimensional linear systems of degree $n$ on
$\P^1$ whose basis realize a fixed number of polynomial relations of fixed
degree, say a fixed number of syzygies of a certain degree. The first result of
this paper is the computation of the dimension of $\frak{X}_{k,r,d}$. In the
second part we make a link between $\frak{X}_{k,r,d}$ and the Poncelet
varieties. In particular, we prove that the existence of linear syzygies
implies the existence of singularities on the Poncelet varieties.

13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn