论文标题
二聚体和Beauville集成系统
Dimers and Beauville integrable systems
论文作者
论文摘要
与凸面上的凸积分多边形$ n $相关联，是两个可集成的系统：由平面二聚体模型构建的goncharov和kenyon集群集成系统，以及与$ n $的圆环表面相关的Beauville集成系统。两个集成系统的相位空间之间有一个名为光谱变换的异性图。当$ n $是三角形$ \ text {cons} \ {（0,0），（d，0），（0，d）\} $时，我们表明频谱变换是可集成系统的生育同构。
Associated to a convex integral polygon $N$ in the plane are two integrable systems: the cluster integrable system of Goncharov and Kenyon constructed from the planar dimer model, and the Beauville integrable system, associated with the toric surface of $N$. There is a birational map, called the spectral transform, between the phase spaces of the two integrable systems. When $N$ is the triangle $\text{Conv}\{(0,0),(d,0),(0,d)\}$, we show that the spectral transform is a birational isomorphism of integrable systems.
