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摘要翻译：
我们考虑了$(k+1)$维线性子空间的Grassmanian$\MathBB{G}r(k,n)$（{\p^1},\o_{\p^1}(n))$。我们定义$\frak{X}_{k,r,d}$为$\p^1$上的$k$维n次线性方程组的分类空间，它的基实现固定数目的固定次数的多项式关系，即固定数目的一定次数的syzies。本文的第一个结果是$\frak{X}_{k,r,d}$维数的计算。在第二部分中，我们将$\frak{X}_{k,r,d}$与Poncelet变种联系起来。特别地，我们证明了线性Syzgies的存在意味着Poncelet变体上奇点的存在。
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英文标题：
《Geometry of syzygies via Poncelet varieties》
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作者：
Giovanna Ilardi, Paola Supino, Jean Vall\`es (LMA-PAU)
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/0806.4881
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