论文标题
离散定期操作员的关键点
Critical points of discrete periodic operators
论文作者
论文摘要
我们使用组合代数几何形状的方法在周期图上研究了操作员的光谱。我们的主要结果是绑定了Bloch品种的复杂临界点的数量，以及在获得该界限时的有效标准。我们表明，该标准适用于Z^2-和Z^3个周期图，并具有足够多的边缘，并使用我们的结果来建立一些Z^2-周期图的光谱边缘。
We study the spectra of operators on periodic graphs using methods from combinatorial algebraic geometry. Our main result is a bound on the number of complex critical points of the Bloch variety, together with an effective criterion for when this bound is attained. We show that this criterion holds for Z^2- and Z^3-periodic graphs with sufficiently many edges and use our results to establish the spectral edges conjecture for some Z^2-periodic graphs.
