论文标题
Feigin-odesskii支架，Syzygies和Cremona转换
Feigin-Odesskii brackets, syzygies, and Cremona transformations
论文作者
论文摘要
We identify Feigin-Odesskii brackets $q_{n,1}(C)$, associated with a normal elliptic curve of degree $n$, $C\subset {\mathbb P}^{n-1}$, with the skew-symmetric $n\times n$ matrix of quadratic forms introduced by Fisher in arXiv:1510.04327 in connection with some与$ c $的距离品种相关的最小免费决议。另一方面，我们表明，对于奇数$ n $，零用$ c $ codimension $ 3 $的理想的发电机给出了$ {\ mathbb p}^{n-1} $的cremona变换，从而推广了Quadro-Cubic-cremona $ {\ Mathbb P}^\ Mathbb P}^4 $。我们使用Arxiv：Alg-Geom/9712022中考虑的转换确定了这种转换，并为反变形找到了解释公式。我们还发现了从Arxiv：Alg-Geom/9712022的Cremona转换的多项式公式，与$ C $上的高级捆绑包有关。
We identify Feigin-Odesskii brackets $q_{n,1}(C)$, associated with a normal elliptic curve of degree $n$, $C\subset {\mathbb P}^{n-1}$, with the skew-symmetric $n\times n$ matrix of quadratic forms introduced by Fisher in arXiv:1510.04327 in connection with some minimal free resolutions related to the secant varieties of $C$. On the other hand, we show that for odd $n$, the generators of the ideal of the secant variety of $C$ of codimension $3$ give a Cremona transformation of ${\mathbb P}^{n-1}$, generalizing the quadro-cubic Cremona transformation of ${\mathbb P}^4$. We identify this transformation with the one considered in arXiv:alg-geom/9712022 and find explict formulas for the inverse transformation. We also find polynomial formulas for Cremona transformations from arXiv:alg-geom/9712022 associated with higher rank bundles on $C$.
