论文标题
兼容的Feigin-odesskii泊松支架
Compatible Feigin-Odesskii Poisson brackets
论文作者
论文摘要
我们证明，与普通椭圆曲线相关的几个Feigin-odesskii Poisson托架在$ {\ Mathbb p}^n $中是兼容的，并且仅当它们包含在卷轴上或在$ {\ mathbb p}^5 $中的Veronese表面中，而$ {\ Mathbb p}^5 $（与$ n = 3 $的例外）。在情况下，$ n = 3 $，我们确定与与普通椭圆曲线相关的两个（不兼容）泊松支架的Schouten括号对应的四分位数。
We prove that several Feigin-Odesskii Poisson brackets associated with normal elliptic curves in ${\mathbb P}^n$ are compatible if and only if they are contained in a scroll or in a Veronese surface in ${\mathbb P}^5$ (with an exception of one case when $n=3$). In the case $n=3$ we determine the quartic corresponding to the Schouten bracket of two (non-compatible) Poisson brackets associated with normal elliptic curves $E_1$ and $E_2$.
