论文标题
关于Bridgeland稳定条件和加泰罗尼亚人数的注释
A note on Bridgeland stability conditions and Catalan numbers
论文作者
论文摘要
在此简短说明中，我们描述了代数几何形状中的一个问题，其中该解决方案涉及加泰罗尼亚数字。更具体地说，我们考虑了椭圆表面上相干滑轮的派生类别，以及其自动等量组对其Bridgeland稳定性歧管的作用。在求解涉及此组动作的方程式时，会出现加泰罗尼亚数字的生成函数，从而使我们能够使用加泰罗尼亚数字的渐近估计来达到解决方案集的界限。
In this short note, we describe a problem in algebraic geometry where the solution involves Catalan numbers. More specifically, we consider the derived category of coherent sheaves on an elliptic surface, and the action of its autoequivalence group on its Bridgeland stability manifold. In solving an equation involving this group action, the generating function of Catalan numbers arises, allowing us to use asymptotic estimates of Catalan numbers to arrive at a bound for the solution set.
